Welcome to the forum.
If this unit is from the 80s, it more than likely has bad capacitors, and is dangerous to use, either to the battery or to the operator. Consider investing in a new converter, a good quality new unit will work much better.
Having two battery connections sounds like it's from a motorhome rather than a trailer, so one output for chassis battery (engine) and one for house battery. Not sure why they would be labeled car battery and trailer battery, that's just odd.
Use a volt meter to see what the readings are on each output. Choosing the wrong one won't likely do anything bad right away.
The issues could be the output voltage is too low, or too high depending on what chemistry of battery it is expecting to be connected, resulting in a undercharged battery or an overcharged and boiled dry battery.