Yep, it grounds to any one of the 5 screws.
Have you checked the splice in the Yellow-Red wire? If this isn't your splice, I would trace the wire from the sender to the gauge and make sure it's good - or test continuity on it.
You can also pull the sender and test it with an ohm meter... or ohms function on a multimeter.
I don't recall what year FJ40 you have... here's what @Downey says the resistance should be:
(a) Up to 9/72 is 100 ohms empty, 3 ohms full, but with a 7 volt drop built into the Toyota sender.
(b) From 9/72 is 120 ohms empty, 17 ohms full, full 12 volt operation.