Here's a great site
with pictures of the internals of a legacy fuel gauge. That might help you understand the problem. Old fuel gauges use coils with very thin wire to create magnetic fields that move the needle based on current flow that creates magnetic fields.
Too much voltage will create far more current than those wires can handle, and they will burn through, making the gauge useless.
Ohms law says V=I*R (voltage equals current times resistance). So, put another way, I=V/R. If the resistance of a wire is 60 ohms and the voltage is 6 volts, then the current would be .1 amps. Increase the voltage to 12, and the current will double to .2 amps. If the wire is rated at .15 amps, it will quickly burn through.
Having said that, to blow a fuel gauge requires a complete circuit. Touching a single post to "hot" while the gauge isn't grounded or connected to anything won't do a thing. Touching a 12 volt wire to the larger post while the case is grounded might well burn the wires quickly.
And, as you can see if you viewed the pictures on the site I linked to, you can feel perfectly comfortable connecting a modern VOM to your gauge to measure the resistance of the coils.
