I had my last trip this weekend, it was a continuation from the weekend before. It was in my friend's empty lot with no hookup. I did this type of trips to get to know my trailer and enjoy the outdoors there. I used a gas generator to recharge the battery and for watching taped movies on a HD TV at nights. I have a volt meter to measure the battery level. I left my trailer there and came back after 5 days, the battery level from full was down to close to 10 volts. My meter as a scale to 10 volts but the needle goes past that when the battery is fully charged. In my observation the battery gets fully charged after 4 hours plugged in. The watt reader is at 170 watts during charging and after 2 hours it goes down to 50 watts (trickle charging), after 4 hours it had a reading of 37 watts which I conclude as power used by the trailer's gadgets including the built in battery charger.
I used the volt meter in the light holder below the microwave oven, it had the same reading when I connected it directly to the battery. When the reading is below 10 volts, you should avoid this because it may shorten the life of the battery, charge the battery to full as soon as possible.
Cheap generator very noisy but it was ok where I was, no campers on site to complain. Look closely to the plug, the watt reader meter is hooked up.
I will remove the fuse from the fuse holder located close to the battery external case, if I'm not hooked up for days and to save energy.
I think this is nice to know that the alarm goes off when the battery level is low. During my testing of battery levels, it was close to 32f and I was using the furnace, before I slept the battery was fully charged and the battery level was down to 11 volts the next morning. I figure the furnace fan uses up the battery and may fail on the second night if the battery was not charged. My cheap generator was good to have.
Good luck on your investigation.