I would test the output of the converter. Disconnect the batteries, then test the trailer leads with it plugged into shore power. Then unplug, hook them back up and test again when plugged in. Tell us what you find.
How old are the battery(s) and what the water level like?
2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.