Will a Nikon or Pentax total station work with a TSC3 data collector, or just Trimble TS only?
Nikon should but it depends how old
Nikon should since Trimble is in a strategic partnership with Nikon for the distribution of their total station.
The older Topcon model GTS and GPT series do not work with some Trimble software. The Topcon ES series total stations do but you must tell the Trimble software the total station is a Sokkia (which it actually is - Topcon owns Sokkia as of nearly ten years ago).
I've never tried a Pentax but I've never had a problem with a Nikon or Topcon. Leica might be a problem; I've seen some that would work but you lost a lot of functionality.
As of a couple versions back Access will also now allow you to Bluetooth to third party guns; I was able to BT to one of our older Topcons a couple weeks ago.