Actually I'm getting a good idea what to do, but I'd apprediate some input.

I found an EXTREMELY (almost identical) sending unit at the junkyard, I tested it with the multimeter and got a solid 0-ohm reading. I could not get it to fluctuate when I manupulated the float. The little nickle-plated resistor/contact appears to be in excellent condition, so I can only assume that the coils are at fault in the junkyard unit.

The sender unit I just extracted from my car is now sitting in a warm water bath, so that I can crack open the float canister w/o breaking anything. Even removed from the car and manually manipulated, I get no reading from the old unit (or I get infinity, either way, the needle on the meter doesn't move).

Based on this and all the other info that Brickboarders have provided me, I'm expecting to see a destroyed little nickel spring thing inside the original float assembly. If I do not, I am going to need some suggestions. The gauge is fine, wiring to the gauge is fine, I've tested the sender unit at the plug end of the wiring, and now at the tops of the two coils, so I'm almost out of ideas.

I'll let you know soon.

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BTW: Getting the original unit out of my tank was an absolute frellin' pain. I was about to give up, when I recalled a post about manupulating the sliding float canister - sure enough it gave the few centimeters that I needed to get the unit out. Fortuantely I didn't lose the filter sock :) Too bad it's friday, too late to get a replacement from the dealer before Monday.
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Volvo #6: all wagons.... 1972 145S, 1976 245 DL, 1983 245 GL, 1986 740 GLE, 1990 740 GL, now a 1995 940...