Above you showed how you connected the TV battery to your camper battery.
If you checkout the post from GeorgeTelford at http://ww.tnttt.com/viewtopic.php?f=30&t=6429, he says the following regarding charging a battery from a TV:
If you were to charge via the vehicle alternator, you would be extremely lucky to get 70% of fully charged, therefore max "safe" useable power is 20 Ah ie you couls use the item for 10 Hrs Max
There is a 4 th rule avoid "charging via an Alternator" this one is much harder to explain, but say you fully charge your battery by Shore power at home, if you drive to your destination with the battery connected to the alternator, the battery will be at 65 to 70% by the time you arrive.
from fully charged at 12.93v (measured 12 hours after coming off the Sterling charger) connected bulb, it took 6 hours and 17 mins to reach 12.2v (ie flicking over backwards and forwards from 12.3v)
It was then fully recharged on the Sterling, allowed 13 hours to settle the voltage, reading was 12.94v flash 12.93v, the engine on the iveco was started, then I connected the battery using a good solid cable as before and drove this morning for 1 hour 14 mins, as soon as I got back it was connected to the same bulb (55w halogen) connected at 12 : 12 today, it started flashing between 12.3 and 12.2 at 5 : 37 PM today
Same battery, same full charge by Sterling, only difference 1 hour 14 mins of extra "charging" as knocked off 52 mins off usable power !!
If I were to just read that post, I would think it would be a bad idea to charge a battery off the TV alternator. I'm curious what you and others think about this.
Joe