The levels in each side of the tank are normally balanced by the in-tank venturi pumps. See this for details:
https://www.the75andztclub.co.uk/for...d.php?t=108535
I can't see how long term evaporation would reduce one side more than the other.
Anyway, add a gallon of fresh juice to eliminate that from the equation. The pump should run whatever the fuel level. I don't think it's clever enough to react to levels. You might check the continuity of power through the motor. Remove the right side tank hatch cover and you'll see the pump/floats system connector. Pull the plug off and use an ohm meter on the appropriate pins (2 & 5) to check that the resistance is OK. If it's open circuit or a vastly different reading from that shown below, then the pump should be replaced.
You might also confirm that power actually reaches Pin 4 when the relay activates.
TC