"Gas water heater timers".... boy, those go back a *ways*.
These were availaible from at least two different manufacturers, AMF used to make such a device called a "QWATERBACK" - I remembered the name (took a couple of days) - and GOOGLE found one still in the box, on eBay, if anyone is wondering what they looked like:
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I have no idea how - or if - this device was effective or safe.
Or if it would be considered an acceptable modification by your WH's manufacturer.
Or by your local building department.
Or your insurance company.
My guess would be that the answer is to all three is no , and if I found one of these during an inspection I'd recommend it's disconnection unless all three approvals could be confirmed - and even then, how would you find a "qualified person" to perform an inspection or repair of such an installation?
Michael Thomas Paragon Home Inspection, LLC Chicago, IL mdtATparagoninspectsDOTcom
847-475-5668