What bothers me is that 13.2 when connected to 13.8. I would normally consider that to mean the battery was low on being connected --maybe even 50% SOC.
The OP says it was 13.0 to start with, so that does not compute. IMO stick an hydrometer in it to remove all doubt. I would at least go camping near where there is a battery store, or else take along a spare. But again, I do not have a good picture of what is going on.
You can have high voltage, but where it does not hold that high on loading. The OP seems to have a clue, so this is just me being a worry wort.