Nevertheless, and I hope this sounds constructive, this is the kind of topic that you should really be discussing with an occupational therapist or child psychologist with experience in autism.
For some topics the internet can be a terrible place for advice.
Meltdown happen when you remove the stimulus without warning. Always, Always give a countdown. Either in time or turns.
So reason - i.e. Time to eat now, 10 more seconds before water is turned off. 10..9.8..3.2.1 Turn off water.
The Autism Society do a LIFE changing course for parents on understanding Autism.
Embrace the water games. Make a clear pipe water feature and enjoy to together.
Hope this helps.
Also suggest swimmming leasons and from there maybe a swimming club.
Saying this as worked for me.
In fact, compare the cost of water wasted to the cost of other inputs in his life.
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What I was really looking for was a science toy I had as a kid, where you could build various types of pumps, siphons, etc. It only needed a sinkful of water.
That has the whole moving water & noise aspect without continuous water intake
https://en.wikipedia.org/wiki/Heron%27s_fountain
There are many YouTube videos that show how to make one using low cost / household materials.
You might have success with a CBT or exposure therapist. If he’s too young a play therapist might be more able to help.
Difficulty would be keeping it safe with regards to electric.
Unless you actually have a cost issue (do the math on that) there already exist a really good water recycling system in many developed countries https://en.wikipedia.org/wiki/Reclaimed_water even if it doesn't exist where you are, water is not lost due to the water cycle. In many places domestic water use is a negligible part of the water supply issue, don't be guilted into messing with your childs development for that.
I would generally teach the children to turn off water after it is done, to not leave the room if water is running and how to prevent flooding and how deal with flooding.
If cost is actually an issue a simple variant to reduce that cost without reducing agency is to have a simple mechanic constraint how far the tab can be opened that is tamper obvious. If those mechanisms are damaged address that issue . Reinforcing is possible but also increases the risk of damage to faucet which is going to be a lot more expensive.
Water toys which use less water but also have an acceptable spilling risk could reduce water use. This could be anything from a digital circuit using water logic that just stops doing something interesting or an analog computer with a limited capacity before it fills up whose drain rate is small or requires adult supervision (lock) to drain. Closed containers with fluids might also be interesting. Such as non mixing differently colored fluids which in a drop proof container.
If you want change the amount of water allowed in a way depending on good behaviour a 3d printing pen would allow to construct tamper obvious mechanical constraints with different amounts of reinforcement which are unable to be removed without breaking in most tabs.
Faucet heads that are designed for saving water often are set-up to create the "feeling" of lots of water, without actually using the same volume (water saving rain style shower heads are particularly good at this).
Something like that would probably preserve any sensory elements of the experience they enjoy and would cut the water consumption by 60-70%.
I don't even know what they did only that it was hours per day for years and year.
I was amazed at his transformation.
On a more helpful note, what about a fish tank pump and a pond or other water holding tank?
Verbal?
Can they look after themselves?
From your description I assume under 14, no, no.
Recycling water fountain somewhere near tiles or a drain if you can afford it. There’s the pot type which has water running down the sides, low maintenance and they’re very, very safe.
For a first step, you could turn off the main house water (assume this is controlled elsewhere) briefly until your child loses interest and leaves the bathroom.
I bet you could pull this off with a container (Like a clean IBC tote) and a well water pump. Have the drain go back to the tote. Setup a sink off of the well water line. It will keep the lines pressurized and usable. Then have the sink drain back into the tote. Would want to treat the water like pool water to keep it from getting gross. a little filter and some shock/chlorine.
It is not a bath tub, but would still let them enjoy a sink.
The pump might be loud if you but a cheaper one which could be an issue for the child.
Might be able to rig a sump in the tote instead (cheaper) but you would need to figure out how you want turn it on since it would always be submerged in water - the normal switch would always be on.
Good luck - would be interested in knowing what solution you come up with.
Edit - After looking around a bit, you can pick up a grey water recycling system. They have the pumps, filters, container all bundled into a kit. This seems like the easiest (but not exactly cheapest) way to go. While speculating above I was basically re-inventing one of these. Also it looks like you can scale this down to an RV sized system or up to whole house.
On a naive interpretation, "recycled tub" is a health hazard.
Clean water is clean because the drain is separate from the supply.
You really really don't want sewage in the water you drink.
And if you put bath water in a potable supply pipe, you will because bath water has had someone's butt in it and pressure differentials create backflows (i.e. siphoning) in the potable water pipes.
Without an air gap, you cannot prevent it.
Part 2:
Limiting the supply would be a simple matter of adding a valve, except that a bathtub has two supplies, hot and cold.
Getting the mix right is safety critical because hot water creates a really nasty type of burn...enough that can kill a person.
Part 3:
There's a reason plumbers are licensed.
It's not greed.
It's because you didn't ask "how do I prevent backflow?"
Part 4:
Putting something connected to mains power into a bathtub is a bad idea.
It sucks if your fish die from an electrical short.
But not like if it were your child.
Part 5:
You could rig up a mechanical pump and let your child pump their own bath water to their hearts delight.
Seems like the simplest thing that would work...where working means not being a health hazard.
As a bonus a mechanical pump can be put in a suitcase and taken into a hotel room.
Part 6:
Good luck.
You can treat it like a pool, which would work too, and periodically clean it.
https://www.homedepot.com/pep/MacCourt-Grand-Cayman-165-Gal-...
My cat (before he passed) loved running water, he wanted me to have the sink running 24/7 or he would yell at me. Fountains helped there.
And he could enjoy having an aquarium or even better a terrarium to watch also. You can easily couple this with a small pump and faucet or with shooting waterfalls that he can touch.
Something like that should be the idea, not necessarily with frogs:
Fill the sink (or a tub) up with 2-4 inches of water, put this filter in it and turn it on. You'll have a small, never ending waterfall on your hands
https://www.amazon.com/Aquarium-Filtration-Reptiles-Waterfal...
you might setup a recycling system and find that since its not the same location it doesn't have the same effect. Part of the fascination could be the snug feeling of sitting in the bath or not having to wear clothing, it could be the temperature in the room, the colours, the light level, the tiles or rugs, the smell or perhaps the mirror or the windows or the room could be a safe place for him such as memories of being bathed when younger and the water is part of that self-soothing mechanism.
You might try setting up a similar experience to the bathroom in his bedroom or another safe space as an alternative option, a bath like container with blankets (or without if he prefers to not wear clothes) you could then introduce a water flowing system or fountain and see if it has the same effect. It may be that the water is only a part of the stim and the soothing effect from the surroundings is a bigger part.
If you take a recycling water approach there are a lot of people making mini kitchens for their kids with a recycling water setup there should be youtube tutorials you can adapt to a container.
Do you have room outside for something like a splash pad or kid pool? Maybe if they're functional enough they can learn that the kid pool is for indulging their fascination but inside water is not?
Do you think they would be interested in an indoor water feature? That could be an option.
Also see if maybe your child is interested in digging deeper into this interest. Books and videos on fluid dynamics are extremely complex and sprawl out into other areas of physics.
Maybe also going out to different water attractions if thats palatable. Public spray parks may be a good option for some variation. Possibly streams, ponds or beaches.
https://www.screwfix.com/p/surestop-remote-stop-cock-push-fi...
My neurotypical 2yo would play with it for hours at a time.