Welcome to the forum
You looking for the CONverter not an INVerter.
Converter takes 120VAC and produces 12VDC to charge the battery, and run the 12V stuff.
There are 2 types of converter, integrated, and stand alone. Integrated will be the lower half of the power distribution panel and you’ll have to remove the cover to see it. A stand alone should be close by and probably behind the panel.
If you look at all the 12V fuses, are there 2 30 or 40 amp off to the left and not in the row? If so those are the reverse polarity fuses and if you hooked up the battery backwards they blow and have to be replaced.
In a stand alone those fuses are on the back side of the converter where the battery leads attach.
If you changed your battery, I would make sure the trailer leads are on the correct posts and then look for the fuses I mentioned.
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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.