I have installed some thin brick in my basement. This is 1/2" thick brick veneer that is glued up on a metal panel. The manufacturer recommends that you use Type S mortar with application via a "bakers' bag". I've tried this and find it very cumbersome and to be honest my forearms are simply not strong enough. Is there a way to apply mortar or caulk via a hand tool (like a caulk gun) that would similate the look of a brick joint?

Yes. I've seen mortar-like stuff in a caulk tube that pretty much looks like normal mortar once applied and finished with a damp finger.

Check your local Lowes/Home Depot/Sears.

Depends on what you think mortar is supposed to look like, lol, no it doesn't look like mortar and it want hold the brick together like mortar either.
You may try some tile mortar, thinset, you don't have to have sand and all that, just add water is all. Mix it a little thick and try that,

Masonary isn't easy, though to watch one do it, it may look that way