Just ask Stan, who has probably toasted at least one Simpson 260 in his day.
Fortunately, I apprenticed at the dawn of the digital multi-meter age. All the journeymen were still using Simpson meters, but I had a $350 solid-state meter with a seperate amp-clamp. The worst that would happen when I tested resistance with voltage applied was a blown fuse in the meter. Granted, it was a special $12 fuse, but it wasn't a new meter.
I shutter to think what it would have cost me had I been buying a Simpson 260 every time I messed up.
Apprentices today have no idea how good they have it. A Fluke 323 does everything a field tech could ever need for $115. The meter can be set to anything (including resistance), have 600v applied, and just shrug it off. Every time I hear about the "good 'ol days", I think back to those guys and their $300 meters (about $1200 in today's money).
For Brian:
I sense your frustration. But once you figure this out, lots more things will be clear to you. I'm going to try again to explain, but as Mitch pointed out-- some stuff is just better conveyed by watching.
1) Electricity always seeks a ground. That's how every electrical "load" works. It doesn't matter if it's a 12 vdc gas gauge, or a 1000 hp 480v/3p chiller. We push power through a "load" towards ground, and the "load" does work.
2) Every electrical device (that you care about, anyhow) is either a switch or a load. In this circuit, the gauge is the load, and the sender is the switch.
3) The sender in this case is a variable switch in the ground side of the circuit. It partially completes the circuit to ground, depending on the position of the float.
4) The gauge in this circuit is the load (electricity does some work-- in this case it moves the needle). Power is applied to the gauge any time the key is on: 12 vdc, all the time. The needle moves because the power is seeking a ground. The amount it moves depends on how much of a ground it finds, because the switch (the sender) completes the circuit variably.
5) You've proved that the switch is fine by checking resistance with the wires disconnected. I think the gauge is probably fine because it moves around. There are three wires in this circuit, not two: power to the gauge, a wire to the sender (which is really a ground to complete the gauge circuit), and a wire from the sender to ground. The reason everybody keeps talking about a ground is because the circuit is completed when the sender creates a variable circuit to ground. No good ground, no good circuit.
That's all I've got. Good luck.