How can I tell if I have properly patched a tube? (specifically a 2" mt. bike tube)
I do like you do when riding, and I usually save up my tubes with holes and patch a bunch of them all at once. That way I can use a tub of water to both find the holes, and can go back through them after patching and test to see if they are holding air.

If I have any doubt after patching a tube, I give it a little time to cure and then I pump it up and hang it from a hook in my garage overnight to see if it loses air.