I too would have the battery evaluated. I would use a
light bulb instead of an amp meter. The amp meter can be confusing and depending on the draw the meter may not have the resolution needed to indicate much. If you can light the bulb you have a draw, it you have a draw that does not light the filament it isn't a problem.
Also I have seen batteries with dirty tops in 6V systems self discharge.
If you are using a volt meter that measures current if the draw is too high it will blow a fuse and it it's a Fluke Meter you will find that t be an expensive fuse
