Can you supply us with a brand and model of your converter? We can then talk better on this.
Not knowing what you have, these converters are not trickle chargers. If yours is original and being a 96 unit, it may only have a normal charge, 13.65 volts and ďmaybeĒ a float charge, 13.25 volts.
From what I know of the mid 90ís units many seemed to be 30 amp converters. They would create a 30 amp DC supply to run lights, water pump etc and give a level of battery charging. And if you had on 30 amps of power in the camper, not that hard to do pending what all you have one at once, then there was nothing left to charge with.
Most of these converters ( the newer ones at least) are sort of setup to only charge the battery at about a max rate of 80% of itís 20 hour capacity rating. And in your case that might be 8 to 12 amps max. They do that I do believe to help control the heat the battery takes on from multiple charges. Pumping large high current dumps into a battery constantly has been know to shorten itís usable life so they on purpose take it slower in the deep cycle systems at least from what I have read in my search to learn about this.
Now you mentioned trying to keep the battery up with a genny on only 3 to 4 hours a day. That can be tricky even on a very high end new 3 stage charger. Charging batteries to full 100% takes a long time. Even a high end charger that goes into bulk 14.4 volts mode dumping a whopping 12 to 15 amps into a group 24 battery can take many hours to get it to even 90% charged. How long to that 90% charged number depends on how drawn down it is. If you only go to the 50% range as good practice pending usage that could take 4 to 5 hours to 90% and then 12 hours or more at 13.65 volts to get to 100%.
Standard RV light bulbs suck power big time. Us that boondock on batteries and a genny have gone into light bulb power miser mode. I myself have 5 LED lights placed in just the right spots as they only draw 0.25 amps for the same light output as a 1.0 to 1.2 amp normal bulb.
If you are going to live in the camper for months on end and never hook to shore power, a solar charge, a total power review to trim excess wasted amps and a new day 3 stage charger/convertor on the genny may be more what you need. And 1 battery may not cut it. I have 2, group 27ís and I have to keep on top of them. Your AGM is better then my lead acid battery but still I have more amp hours available.
Iím not saying it is impossible to get by on 1 group 24, but you will need to count up amps used and make sure do not drain below 50% state of charge and then bring it back up.
Hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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