My 1990 Mustang used a voltage regulator to reduce to six volts. It is a little PC board that snaps into a slot with four contacts, mounted behind the speedometer. Six volt gauges are very common on modern cars.
My '55 Customline's fuel sending unit has a contact, current limiter, and bi-metal strip inside. Power starts at the gauge and on to the float unit, then to ground. The float arm pushes on the bi-metal strip to vary contact cycles. There are NO resistors, NO dash regulator, and my system is 6-Volt, pos. gnd.
Yours might use the same technology. Using a VOM is very confusing because the sending unit contact is either closed, or it's open. Again, there is no rheostat or variable resistor, just current heating a bi-metal strip (kinda like your turn signals, only a lot less current).
With a full tank, the contact is constantly closed, pegging the dash gauge. At half full, the contact is open and closed in equal cycles, making the gauge read 'half.' When the tank is empty, the contact is always open, no current flows through the gauge, and the pointer rests at, 'EMPTY.'
Check it out:

Note the snail-cam inside for adjusting "1/2 Full" scale. It pulls (sets) the top contact higher or lower, adjusting contact closure frequency.
I couldn't believe what I was seeing when I first opened this sending unit. No wonder they went to a cheaper rheostat. Cold ambient temperatures tends to show more gas on this setup. By the way, that current limiting resistor corroded, causing this unit to fail (open). Hope this helps. - Dave Dare