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Nice try, but we are not told if the mirror is moving toward us or away from us, or what, and I think that would affect the results -- if such a problem even has results.

Thanks for the encouragement. :)

In my guess, I made the assumption that whether the mirror is moving away or towards us doesn't make a difference since "the mirror is located 1/2 light year away when the signal bounces from it."

In my guess, I made the assumption that whether the mirror is moving away or towards us doesn't make a difference since "the mirror is located 1/2 light year away when the signal bounces from it."

Quite right. I had forgotten that.

In my guess, I made the assumption that whether the mirror is moving away or towards us doesn't make a difference since "the mirror is located 1/2 light year away when the signal bounces from it."

But it does make a difference. This is because in the frame of the moving observer, the distance between the two events (signal transmission and signal reception) is different, and the time between them is also different. (For a signal moving faster than c, the time ordering of the events may even be reversed.) For a signal propagating at the speed of light, these changes work out such that the speed of the signal is invariant for the two observers, but that's the only velocity for which that can be arranged. Anything moving faster or slower than c will have different velocities with respect to the two observers.