Had the same problem on my 66, with a converted 12V system. Battery would die after a month.
My problem was that the starter windings were burnt, therefore took a lot of juice to start the engine, check the positive wire when cranking the engine, mine was very hot.
When I opened the starter, I found the windings burnt, the starter turned also very slowly, after the overhaul, all was ok, no more dead batteries.
Good Luck
PS. Check to see first if your alternator/generator is charging properly.