Alton Brown has a recipe for Gyros on his web site. I made it and it was pretty good. He offers two options: cook it as a loaf, or compress it into a log tightly wrapped in plastic, firm it up in the fridge overnight, and then stick it on your rotisserie rod and turn it. I did that, and it worked.
We're visiting our daughter & family in Pattisburgh, and last week caught the Greek food fair at a local Greek Orthodox church. About the best Gyros I've had, and there are some good ones in Chicago!
Interesting point- they're called HEE-ross in Chicago and JY-rose in Pittsburgh. And the speakers are all Greeks.
But- there's gotta be a LOT more garlic in the Tzatsiki than what I see up above.
Mike