weird electrical starting problem

I am having a starting issue on my 1982 xj 750 maxim. I chopped it down to nothing. Removed all electrical to what is just needed. headlight tail light starter and ignition. I finally got it ruuuning after rebuildign cleaning and jetting the carbs. It wouldnt start unless
I was jumping it off my car battery. So I went and got a new battery for it. After slowly charging the battery overnight the bike fired up with no issue. I took it for about a 20 mi ride. After that i let it sit for about an hour. It started right up again with no problem. Went to the gas startion from there got gas and it didnt want to turn over seemed liek the battery was dead. So I push started it and it fired fight up. Rode it home with no issue. When I went to start it the next day same thing. Seemed like a dead battery it wouldnt turn over. The headlight and tail light were on so the battery wasnt dead. jumped it iff my car and it fired right up. When I took the jumoer cables off the bike died right away. The headlight and tail light still on. I am confused on this and any help would be great

 

Sounds like you are running off straight battery and no AC Generator (same as your car running off battery and no alternator).

The battery will have enough charge to keep your lights on but not enough juice to turn over a large draw item like your starter.

So - check your generator and check your entire charging system.