I have recently returned from a touring holiday around Northern Spain with 4 other M3W's. One of them had an Exide AGM 12-31 battery that had been fitted 3-4 years ago and had caused no issues in that time. Following reports of problems he had it checked by the Morgan workshop that he had do a pre-trip service, it got a clean bill of health.
A few days into the trip the indicators and tacho failed, along with some hesitant engine running. We disconnected the Turn Signal Module, no indicators or tacho but the engine ran better. The engine cranked over and started easily every time. We tried but failed to find a replacement battery, so set out on the trip to the next hotel in convoy.
Almost at the next hotel the engine cut out and there was no electrical power other than the chattering of the fuel pump relay when ignition was turned on. A power pack battery across the battery terminals confirmed the battery had failed by restoring full function. We got the stranded M3W back to the hotel with a battery robbed from another M3W. A replacement was found eventually at a Stihl garden machinery dealer who had 5 in stock! They are used on mowers and small tractors, worth remembering if you need a battery. This worked perfectly for the rest of the trip.
I would suggest that if you have one of these Exide batteries fitted, no matter what age, replace it. I am not sure if the failing battery took the TSM out but some have had rectifier failures at the same time as battery failures, so some electrical power spikes are likely causing secondary damage.