Does your fuel cut-off cut off?

That sounds like a fuel supply problem due to a very low sitting rear tank. Basically there should definitely be an electric fuel feeder pump right in front of the rear tank. Pumps are very poor in SUCKING fuel from low down, so the engine driven pump will struggle or be unable to feed fuel into the engine in that situation. Electric feeder pumps are standard in many low wing aircraft, rightly so. I urgently suggest fitting an extra pump in the fuselage for including into take-off procedures. – Or else you will risk to end where you did not want to go. Better to be illegal but alive than to be legal and end in the woods upside down. Your mechanic will be capable of setting up a bypass system of extra pump and one-way valves in the line so after switching off the electric pump there is the normal routing of the fuel to the engine. Vic

Not my plane unfortunately (bigger house mortgage came first), but I’ll have a chat with the owner next time I see him

Has the finger filter in the rear tank been checked? Does this happen even with the electric pump on?

Maoraigh
I believe the whole fuel line was checked, and the warning light only usually comes on when the pump has been switched off