How do I know which is the correct AI to connect to a system's "Synch Out" pin?
It's up to the computer software. A DAQ is just a way to get signals into a computer. It doesn't care what the signals are. If you are looking at a signal as a graph on your screen for example, and you look at AI 2, but your signal is hooked up to AI 1, you won't see it - for obvious reasons. If you moved the signal to AI 2 or switched the graph to display AI 1, you'd see it.
So it depends on what the computer is doing. This can't be answered based on only the electronics side.