After getting desperate for an answer, I started calling around to local arcade rentals and repair shops. Here's the answer in case anyone else runs into this in the future:
One of the repair techs told me that those fuses attached to the underside of the T2 control panel are to protect the guns internal coils (which make the guns vibrate) from burning up. So Player1 is wired correctly & Player2 is incorrect. Technically, Player2's guns MIGHT work without connecting the red wire to the fuse (I dunno for sure) but I run the risk of shortening the life of that coil if I leave it that way. So, in this case, I have to splice Player2's red wire (which runs from the internal coil down & out of the bottom of the gun housing) and attach it to both ends of 1 of the fuses installed under the control panel.
Not sure if it matters which direction the wire should run through the fuse connections, but I guess I'll find out one way or another.