Since the center snapping the ball doesn't provide any sound, how can it be analogous to the starter's gun? The LT is watching the pass rusher in front of him, not staring to the right at the center. So, Watson has to be the starter's gun.
To my knowledge, the only time the other OL would be looking at the center would be when they are using a silent count, otherwise, the QB is the starter's gun.
Jeff Saturday used to make the OL calls for the Colts.
DW4 makes the OL calls for the Texans.
Although a good C is a staple of any good OL.