Like Ela1948 said... charge them individually.
Mark the battery that had the lower voltage, for future reference. When you finish charging the first battery, the voltage should be about 13.2 volts. Disconnect the battery and let it rest (no load or charge) for either 24 or 48 hours (I prefer 48 hours), then test its voltage, it should be at 12.6 or higher. Using the same charger, do the same for the other battery and take its voltage reading at the end of the rest period. The voltages should be within .1 or .2 Volts of each other at the end of the rest period. If they are both about the same voltage, I would then put them both on the charger and top them off before putting them in the TT. Make sure you check the water level on the batteries, especially the lower voltage one. I would keep a close watch on them for a week or 2.
The best way (most accurate) to know if your batteries are OK, would be to go to an auto parts store and pick up a Specific Gravity tester, and after the rest period, test each cell against the mfr specifications... this is the best way to see if the battery is good. You will see if there are any damaged cells.
If they are OK, fully charged and are "Deep Cycle" Flooded Lead Acid battery types, see if there is any way that you can EQUALIZE each battery. Equalizing is actually over charging a battery (between 15 and 15.5 volts) for a specific amount of time as determined by the mfr. It reverses the build up of negative chemical effects like stratification (acid is greater at the bottom of the battery than at the top of the battery). It also removes sulfate crystals that might have built up on the plates.. (which reduces the battery capacity)
Now for the bad news.... If one of the batteries is no longer usable and you are going to replace it, you need to purchase 2 new batteries. If you replace one, the old one that was discharged will eventually bring the new battery down to its level and its life will be about the same as the old battery.
Lastly, keep checking the water levels while charging (safety glasses) and feel if the battery is getting hot or starts to boil, if so stop the charging.
2013 Jayco Eagle 284BHS
250Watt Grape Solar Panel, MorningStar MPPT 60 Charge Controller
1500 Watt Ramsond PSI, 2 Trojan T145 Batteries (260Ah)
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