Some clarification of terms will help us help you. Plugged into 120VAC, your trailer batteries should be charged by the "converter" in the trailer.
The type of converter used in the '80s typically was a "dual-output", so named because it had one section to power the trailer's 12VDC circuits (lighting, furnace ignitor/blower, water pump, etc.) and a second to charge the battery when connected to 120VAC. When 120VAC was disconnected, a relay switched the house 12VDC circuits to the battery.
Contemporary converters are "single-output", where the converter is connected only to the battery, and keeps it charged when connected to 120VAC. The battery powers all 12VDC circuits whether or not 120VAC is connected. You can replace your converter with a single-output (recommended, as new ones have features that allow continual connection to 120VAC, and can actually maintain the battery including desulfating cycles - and your OEM is ready for an Antique Tag), but you may have to jump the old charger output connections to the battery to the single output of the new converter.
Anyway, your suspicions that the prior owner disconnected the converter charger section from the battery are well-founded - because you mentioned the battery worked for 3 days after you charged it with an external charger. The battery appears to be good, but it seems the converter's charge section is kaput - or it's been disconnected.
Some trailers used a manual switch to connect the tow vehicle's power to the batteries (but this is unlikely in your case) so the tow vehicle wouldn't drain the trailer house battery and vice-versa.
3 day's usable power from a single trailer battery is actually pretty good. (I have 2 6VDC golf cart batteries in series, and I can run the TV, satellite, laptop, and lights for about a day, which is a pretty heavy load).
Concerning the fact that the tow truck wouldn't charge the battery: The suspect connection would be pin 4, the 12VDC connector; if the lights, etc., work, the ground can be ruled out.
Anyway, I'd suggest you have two issues:
1. The converter's charging section is disconnected or not working (it may just be the cutover relay has failed- meaning it's not switching converter output to the batteries when plugged in).
2. The 12VDC (pin 4) is not receiving power from the towing truck, or if it is, the connection to the trailer battery has failed.
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