Sounds like the TCU codes need to be pulled. I haven't looked in a long time whether these have a "memory" mode or diagnostic mode or not but I would wonder if you can learn something even if it's not tossing an active code, from a memory functionality or pending code like the ECU.
No there's no fuse. Sorry if you already know this, I don't know if you do or not. Are you sure the TCU light isn't blinking - it only does it immediately at start up, really fast and is easy to miss. It's not like the check engine light which stays on all the time. If you don't look right away at first start up, you won't see it.
It seems unlikely to go into fail safe mode without a code but stranger things have happened.
Have you tried turning it off and restarting it multiple times - does it do it every single time?
I assume the fluid level is fine?
Check the trans pan and make sure it's not dented at all, even a tiny bit. There's almost no clearance between the pan and solenoids, wiring, and sump.
Rodent damage is unlikely but I've seen it more than once. Chipmunks, even in squeaky clean residential neighborhoods, can crawl into areas and gnaw on wiring that's unseen. I've seen wires chewed under carpeting that seemed impossible to access. But this is, of course, unlikely.