The converter charger come into play when the trailer is plugged into a 120VAC connection. It's purpose to power the 12 VDC system while connected to shore power. The secondary thing the converter does is charge the
battery, which is used when NOT connected to shore power.
The biggest concern for older converters is "over charging" the
battery. Over charging boils the fluid out the
battery thus destroying the battery. It's not a problem as long as you keep filling the battery with distilled water and don't let it get low enough to expose the plates.
I have eliminated any problems with a converter by eliminating the converter. When at home I keep a Battery Minder connected which keeps the battery fully charged and does a desulfating operation at intervals. When camping for more that 4 days I have a 65 watt
solar panel that charges the battery. The battery gets charged another way, when under tow the tow vehicle keeps the battery charged.
I hope this helps in some way.