I think the issue is the ECU is not shutting down. The light stays on regardless of the doors being locked or unlocked.
On my BMW the ECU shuts down in stages with what I believe are to slowest to reboot items shutting down last. This way you can stop the car than then jump back in without the car shutting down completely. The car also starts booting up as soon as the doors are opened with the remote.
I suspect that whats happening is that the Morgan / BMW engine management system hasn't been designed / can't shut down fully and hence the light and what ever it indicates staying on are the battery draining. Simply bad design on the management system.
I think that you have hit the nail on the head. My understanding is that modern ecu's do exactly as you say and actively manage battery life by doing so. I am sure that the BMW boffins would sort it out in a couple of hours! Audi say that their battery management system means that a battery can never go flat. I never put the battery on the Aero 8 to the test and used a trickle charger routinely.
