nah, I don't think so.... I'm pretty sure I remember seeing a 2 pin male connector on the side. After looking a bit at Delco remy documentation it seems more and more to be a 12SI model... Which has a internal regulator (System Integrated)...

I'll confirm tomorrow, but it seems I may be able to get away with a GM alternator (like you said), that was used between 1975-1985...

To answer your question, yes the battery eventually drains down when the liftruck is being used alot.... Seems the more it is used, the more the battery gets taxed since the alty do not charge it enough... It is worst if it is used many short times during the week... not so much is it is used on long period (I guess the battery takes just enough charge to hold a bit more like this...?)