I had a friend that was from Nigeria...
She made this fabulous Goat Stew that smelled fantastic, and tasted wonderful!
Goat is a tougher meat than say chicken, but I don't remember it being gamey like pheasent, or even kangaroo... yes I've had kangaroo!
(What can I say? I have eaten all types of international cuisine!)
I thought gyros were made with Lamb not goat! (At least all the gyros I have had were lamb based)
I don't think you can cook goat like grilled, but since it is tougher it needs to be slow cooked or made into a stew/soup. .. so it can simmer for a long time.. to make it less tough.
You're adventourous Barry! Take a chance!