Battery question

In the end, I just decided to get a new battery.

Thank you everyone for your help

Mike

^Tue story on corrosion of the cables and connections.
Recently had an electrical issue with an older vehicle. Everything clean, look like new etc. good battery alternator etc.
After checking all the grounds, took pos cable off battery and it was super corroded and arcing. Did a bunch of cleanup on it and good as new.

10.5 volts should make lights work, barely, so 12 is plenty, but yes, volts and amps are different. It could be a dead battery that just does not have enough amperage to do anything. Death could come from not holding voltage or from not having enough amps.

Take to auto parts store for the free charge n check.
You likely damaged it over the winter, most likely you did. If you let it sit all winter not being charged, then you might as well just buy a new one. Some "chargers" will let a battery die also, they just do not give the battery the right voltage and cannot regulate the voltage according the the State of Charge the batteries are at. Over-charging will do damage also.

Get a real deep cycle battery, not these marine ones. They are called Golf Cart batteries typically and are about the same price.

Cleaning the terminals is huge huge too. Sometimes the battery cable under the cable coating can get corroded and green and not conduct the electricity too, but this is unlikely in your situation.

***edit*
I reread your OP.
"12.5 VDC at battery and 13.75 VDC on wire leads from trailer"
after a day if the batter will not get past 13 (assuming you have a modern and decent charger) then the battery just will not take a charge and is dead. If you leave batt unplugged for a day then I bet voltage drops even more. The 12.5 yo uare seeing might just be a "surface" charge.

I had a battery that I kept charging and would pass my multi meter voltage test but would not work when connected. I didn't realize that the battery could pass voltage but fail under load testing. HF has an inexpensive load tester or the auto parts store as mentioned above.

Test the batteries.. I have my own tester but you can get 'em tested at ye old auto store.

Make sure you did not flip the disconnect switch to OFF.

Something is strange. Baytery might be toast but your converter and the battery at 12.5v should fully power the lights. Fix the bad terminal first.
Also unhook the battery and see if it maintains voltage for a day or so.
Have battery tested.
And you can try charging it again with something that puts higher voltage to it if your converter is only charging at 13.7.

I think 13.75 volts is too low to revive an unhappy battery.
I have a Black & Decker smart charger that automatically goes up to 16 volts when needed. It also has a desulphate mode. It works very well!

I used to keep the batteries in the house but they got too heavy. I live in northern Alberta. Now I leave them in the motorhome and disconnect the batteries when not using them for more than a day unless the solar panel is keeping them fully charged. They stay over 12.6 V for at least a month. I’ve had poor results with trickle chargers.

Also you can try a real charger. Something like a garage will use. Sometimes you need to rock the batteries world.

I do clean the posts, but now that I think of it the positive lead wire was rusted, I will cut back the wire. Battery had plenty of water.

Thanks everyone
Mike

couple more things you need to do, all great advice above. buy a battery tender ,for when tt when just sitting . theres always a little battery use when the tt is just sitting in the drive. and always check the water every three months.