Just to clarify, some MGFs have fuel gauges that return to zero on ignition off. This causes endless confusion because both systems are in place. So, just be worried if the needle never moves even after 100 miles or so.k My MK2 F is a returns to zero type.The fuel gauge reads even when ignition is turned off, so seeing a half full (or half empty depending on your outlook on life is not a concern.
However if you have "brimmed" the tank, and it still only shows half full (or empty) then there is a problem.
Any electrical fault at the rear can be caused by the wiring at the boot hinge, so always worth a check as Graham has indicated. Cut back the plastic cover and inspect carefully.
To test the wiring/gauge you need to disconnect the wiring to the sender, and short the sender wire to ground. It should move 100% one direction (cant remember which way) and when disconnected it should go 100% the other direction.
If it does this then the wiring and gauge are OK and the fault is the sender unit.
Alternatively you could remove the pump/sender assembly from the tank, and move the float by hand and see if there is full movement of the gauge.
One fault I have had was with the wiper arm that presses against the windings in the tank was loose, which caused an always "mid position reading". Just gently bending the wiper to the windings to make better contact fixed it.
Peter