You can make Hydrogen from water at home with a very similar setup, albiet much larger and using much more electricity, and still producing very little useable fuel, at least not all at once.
You sure as hell can't do it under the hood in a mayo jar using a 12V battery, at least not in enough quantity to actually do anything.
I wish I could find the article, years ago there was an old guy around here(Iowa) that was making hydrogen fuel for his truck. Had a huge vat in a shed, powered by a wind generator, and some sort of collection system that he gathered up and stored the hyrogen with. Been years ago, so it's hard to say where I even saw it at.
It can be done, but so can running your car off of golf cart batteries, and you can make your own ethanol too, but none of these can be done economically on a small or large scale. If they could we'd be seeing it.