The factory changed the circuit in September 1982.

Prior to that date the light would only come on when you had 3 gallons or less fuel left. From 9/1982 the light comes on when the ignition is on but before you start the engine, as a check on its function. It's less bright in this check mode than when it is indicating low fuel.

Thus, if your light only comes on at 3 gallons and your car is pre-9/1982, everything is functioning as designed.

This applies to the W123 and W126 (yours) chassis.

The factory did not always get its logic right the first time....