Yet another brilliant subject, Mike.
I own two Tradition watches. They were made for and sold by Sears (as were another obscure brand, Baylor). They are of quite decent quality, with Schild movements. The diver (of which Art might have a picture) is very nicely made; the other, a dress watch, is less so but has such a fascinating screw-down back that I picked it up for a few bucks just to see how it worked. It works by placing the back in position, then screwing in a peripheral ring. Result: the back is screwed down, but the gasket has not been subjected to any twisting force.
Nivada Grenchen actually was a fairly well known brand, with both dive and dress watches. Quite decent quality, with from what I can tell mostly ETA movements. Some of their diver's watches attain a low level of "cult" status.
I have looked at some Sicuras. Some are nasty, one-jewelled affairs; others are not particularly refined but still contain 17-jewel Swiss movements. I think there is some sort of rumored connection between them and Breitling, but it may be sales puffery.
I believe Candino and Technos are modern watches that use mechanical movements.