Power problem

I am having some issues with electical power. I only ride my bike about once a week now and everytime I go to ride the battery was dead. I read that if you leave it sitting it could lose power so I jumped the bike with my car. I had the battery put on a trickle charger and it still had problems, so I decided to just buy a new battery. Well, I am still having similar issues and don't think it is the battery. When trying to start, I can hear the starter turn a couple times, but then it seems there isn't enough power and just clicks like a dead battery. If I am motivated I can still push start and it runs fine. I also noticed that all the lights are pretty dim when idling, but when it is above 2K rpm, they are bright as can be. Does any one have any suggestions on what might be happening? About 2 inches from the positive battery lead, there is a small cylinder, what is that for? Could it be bad? Thanks for the help.
Alex
1982 XJ650 Maxim

 

Something is draining the battery. the PO of my nephew's bike put a toggle switch in the path of the ground from the battery to "cure" a similar situation.


That cylinder is the starter relay.

 

sounds like crud and corrosion
start taking electrical connections apart and cleaning them up
start with the battery - wire, it goes down to the back of the motor, shine up the connectors and put some dielectric grease on them
then do that starter relay then the starter
while your at it just do all the electric connections on the bike, some of the plugs might not have been touched for 30 years
unplug the plugs, blow out the dust, replug 3 or 4 times, put some grease on the pins, replug 3 or 4 times, do the next one
it might be fuse block time too