Welcome to TM KimLake, what you describe is fairly normal for a Morgan of that era
You could potentially have a sticking sensor in the tank, but that's fairly rare
there are electronic gizmos you can add into the circuit and re-calibrate, eg
https://spiyda.com/gauge-electronics/the-gauge-wizard.htmlHowever, most of us just brim the tank, reset the trip and refill at say 250 - 300 miles (Mog model and engine dependant)