Do as Don says to check for a small current draw .
I've seen the ' GEN ' light glow very dimly if a diode fails .
If you don't find any parasitic draw, check out the battery .
How old is the battery

Serviceable type, or sealed

If you have a serviceable type battery, check fluid level in the cells .
You can also have electrical ' leakage ' between the battery terminals from conductive deposits on the battery case .
Set your multimeter to low volts DC scale, place one probe on a battery terminal and the other on the battery case away from the metal of the other battery post and see if you have any voltage reading .
If you do, use baking soda to remove the electrolyte deposit on the case .