I bought a $5 Battery maintainer on eBay. The wires to power and battery had to be replaced because the insulation cracked in cold weather. It has 1 amp maximum and actually charges a battery given enough time but then the current is virtually zero and the voltage rises over 15 volts, which makes me fear for the thousand dollar vehicle computer. Got a $15 one at a local auto store which has voltage regulation to a max of 13.6 volts, half an amp. I think this is a good maintainer but it would take days to charge a battery discharged half way.
Check the voltage provided to the battery by your converter. If only 13.6 V it is just doing what my $15 maintainer does. A good one charges at 14.4 to 14.8, then drops to 13.6 to maintain.
X2 on the solar. I put a 100 watt Renogy kit on our small Motorhome and that keeps the batteries always over 80% when boondocking for a week in summer. We have modest electricity needs with no inverter or TV, Of course always 100% charged at home. Solar charge controllers typically provide the 14.8 v for optimum charging.
I didn't know what was going on before getting a battery monitor and the first pair of batteries didn't last very long - the voltage chart for battery charge level only works several hours after charging has stopped. This cheapo monitor displays the % of full charge all the time by counting amp-hours going in and out of the batteries.
eBay $30 battery monitorIt is a little hard to install; a little electrical knowledge and skill with wires is necessary.
2004 E350 Adventurer (Canadian) 20 footer - Alberta, Canada
No TV + 100W solar = no generator needed