There is no coil under the kick-off switch. The rod is supposed to move up and cut power to lock relay if the bottom of game is kicked.
Check each and every relay and solenoid coil for burnt or brownish wrapper paper. If you find one, check its ohms. Also look at the bottom board relays, there might be a loose screw from playfield landed on some relay contacts.
I am not sure if Gulfstream has DC bumpers, if so, check the rectifier bridge on playfield underside. Temporarily remove one of the AC~ side wires and if the fuse then doesnt blow, you found the problem.
Edit: Looks like it indeed has DC bumpers, so try disconnecting red wire from the rectifier (near left flipper).