I like that relay idea on power wire.
Could it be used on ground wire? Is one method preferred over the other?
Don’t do it on the ground wire. If you lift the amps main ground and the amp tries to ground through the RCA cable shield, you can damage the head unit / RCA cables. This may vary from amp to amp and or may not be an issue, but best to just not do it.
And if this is done, be certain to get a "high amp 12v contactor and or solenoid" instead of a regular relay on the + power wire. Use a smaller relay to turn on the high current contactor if needed. You would overheat a typical relay's contacts with a large amplifier pretty fast.
Hard to say with the Taramps, not sure how they do the remote turn on since the amp uses a microcontroller. Older amps would be easy to troubleshoot. I got a Massive Audio amp in for repair years ago that wouldn't turn on (opposite I know), and had an "open" transistor in the remote turn on circuit, was a simple fix. The Taramps might be similar in this regard, or uses the MCU to do it, which might make repair difficult to impossible without a new MCU. I have steered away from buying any Taramps as I doubt they will sell me an MCU if it needs to be replaced, or it will be priced insane making any repairs uneconomical. I'm still not a fan of amps that use a proprietary microcontroller.