Go into the setup, and there is a whole test for just the clock. IIRC, there is a box for when each opto trips as the hands go through it. As long as your motor and gears or working, I'd start in that test mode.

This is something you should physically be able to see. Not that it matters, but I've never heard of this. Of course it's a problem if the hands aren't going through the optos, but that means something else is wrong and I'm not sure tape is the fix.

Intermittent issues could be a connector, or the pins on the board. I don't suspect the pins as much because you said the board was replaced, take a good look at the connector. Wiggle the wires and test for continuity, see if you have a flaky connector.

(the connector that plugs into the clock board)

I don't, but I just got TZ again I could check.

This board, that board, this is why I almost never recommend people replace boards. Sure, if batteries take out 1/2 a CPU board replace it, but this stuff is almost always so fixable, it keeps it original, and it saves money to fix.