Great time for a pmgr starter (permanent magnet gear reduction). Get one from a mid 80’s FJ60. Vendors here sell them and there are local auto parts house or online options. Bolts right in.
Dang I almost said it sounded like a starter spur gear hitting flywheel!
I had a ski do snowmobile...
Post lots of pics of your engine bay, trans, front driveline, radiator, apron to fender bolts, splash shields, basically everything. A noise like that you should be able to find if external. If it’s internal to the engine, chaos is soon to show itself.
A bad throw out bearing or improper...
Yes you can pop that cover off, no oil in there (unless your rear main leaks!). There, you’ll find your flywheel, clutch and associated parts.
That last engine mount pic: something’s not quite as Toyota designed it…