Find the diagram pasted on the inside of one of the machines covers. Then trace out the gauge circuit. If you have a Ranger 250 GXT The fuel gauge should have 12vdc on terminals 1 and 3. 2 is the input from the sender in the tank.
Start /run switch must be in run. 12vdc starts at battery goes through circuit breaker and then start / run switch. Fuel tank sender should read 240 to 265 ohms empty and 20 to 35 ohms full. If your unit has a plastic tank, look for a ground wire from the sender to frame.
Always post the machine code number with questions on Lincoln welders.
That way we can pull up the right information for your welder and not have to guess.