my thought: I don't think this needs to be posted in 3 places, if you look around you'll find many threads about gas gauges and senders and the simple, direct way to trouble shoot them
that tester is simply a sender in a package to allow dealer mechs to avoid taking out the sender to do the test
if your gauge doesn't work, check the [removed] sender with an ohm meter, should go from 0-30 ohms - if it does and the gauge doesn't respond to manually moving the sender, then the wiring or gauge is bad - if you've eliminated problems with the wiring, you need a new gauge not a new test device

Bill