Ok, the problem is bound to be its old. Green lights are a waste of time so ignore it, your "fully charged" 12.4V is also wrong, it would be about 12.6V. Each year your battery will get worse, I say about 5-10%, I have tested this on many lead acid battery types in the past (not lithium). IF it is 6 years it is good,lots of leisure batterries are only guaranteed for 2-3 years, most people are unaware that the battery is getting worse as they do not load test them(not that difficult), when you "full time" they become very important so I always tested against the same realistic load once a year, it pays off. Hope thats useful