Meaning of "watch your six"

Your intuitions are correct; the phrase 'watch your six' does indeed mean 'watch your back'.

It refers to the 6 position on the face of a clock. If you were standing in the center of a clock face, facing the 12 position, the 6 position would be immediately behind you. From Wikipedia:

Using this analogy, 12 o'clock means ahead or above, 3 o'clock means to the right, 6 o'clock means behind or below, and 9 o'clock means to the left. The other eight hours refer to directions that are not directly in line with the four major directions.

This phrase is often used by combat fighter pilots to refer to keeping an eye out for enemy attacks coming from behind.