Mine was in a similar condition. Yes, the sending wire runs under the cab through that hole in the floor, joins the harness and goes to the gauge on the "F" side (at least mine did). The "E" side went back to the On side of the ignition switch.
My original harness had a ground location down there as well, didn't seem like a good place for a ground so I moved mine when I put in the new harness. I'll try to take a pic for you.
I think that the gauge will peg "Full" if the ground is removed, could be confused about that though.
Good luck!
