Time Machine disk keeps unmounting itself

This is very strange and I will go into as much detail as necessary to get help here. My Time Machine disk keeps randomly un-mounting itself, resulting in Finder complaining that it was not ejected properly, and of course missed back-ups.

Late-2012 27" iMac (yes, its old)

Internal drive replaced with 256GB SSD (boot, user dirs only)

USB 3.0 external for data, photos, music, etc.

USB 3.0 external for Time Machine (3 years old)

Latest version of Catalina and all software

All drives pass First Aid

First obvious culprit would be the 3-year-old Time Machine disk itself. So... replace it. Bought a bare drive from Other World Computing and put into Thermal Take Duet drive dock with a different USB 3.0 cable. But... same issue.

Hmmm... bad USB port on the iMac? Switch to a different port. Same issue.

Hmmm... but the data disk never exhibits this problem, and its a USB drive too. Interesting.

Run HW diagnostics, except it won't launch on this machine. Searching other forums here tell me this problem has no solution. Take to Apple store for diagnostics instead. Except they are closed...

At this, as odd as it seems to me, this is a Time Machine problem. Two different drives, different cables, different ports, different controllers, all exhibit same behavior. But a different USB drive, not used as Time Machine, does not behave this way.

Really don't want to buy a new iMac, even as old as this is, but at this point am I looking at a possible hardware failure? Thanks.