On board battery monitor

it's true that after fully charging a battery if will have a false high float on it, and does not represent it's "resting" capacity.  Wait a few hours after charging for true readings, however this can be difficult unless you are at home and a trip is not imminent.

 I also own an OTC 3181  130 amp load tester. It is for 12 volt automotive batteries.  A simple heater wire device with a meter and a trigger, and two battery clamps, positive and negative. Connect to a fully charged battery and pull the trigger for 10 seconds, the  meter should remain in the good zone. It it falls into the "not good" zone then the battery is not able to take a full charge, and is either sulfated because of loss of electrolyte over time, or it's just worn out and tired. I do this test each spring before the first trip, as long as the batteries check good, I recharge them after the test to top off before installing them in the R-Pod. Check fluid level several times a year, and top of with distilled water as necessary. 

I recommend you instead install a small inverter and get it wired to provide power to the TV instead. I installed a 400 watt inverter under the dinette bench where the converter is. It has an on/off switch, cost $40, and has a USB charge port also for my phone (which is 99.9% of why I have it). My LED TV is a Wal-Mart whatsit brand I bought for $60 about 4 years ago. It has a max power consumption of 22 watts. 

 If you really want to run a DVD player too, that would use a few more watts.

 What I'm saying is, a regular small 120 VAC TV is better than any 12 volt TV by a long shot.