Originally Posted by azflycaster
The 14.1 was not the battery, but the output of the charger. Fully charged is around 12.6-12.8, so 12.5 is pretty close (90%) plus there could be a small inaccuracy in your measuring device.
All the above is 100% correct. It will take the battery a couple of hours after you take off the charger to stabilize and for the voltmeter to show 12.7 volts (i.e., fully charged.)
If you put the batteries into "store mode" the only parasitic load you will have on them is the propane detector which will slowly discharge the batteries over a several week period. If you want, you can disconnect the battery cables entirely from the trailer to save yourself even that small discharge.
Keep an eye on your battery voltage when the trailer is in storage and so long as it stays above 12 volts or so you will be fine. There really is no need to keep a trickle charger on the batteries at all times. Obviously you'll want to charge up the batteries up to 12.7 volts before you take the trailer out camping.
Eventually, you'll probably want to consider some kind of solar set up. They range from fairly simple/inexpensive trickle chargers costing a few hundred dollars all the way up to $10,000+ systems for extensive boon docking with little compromise in electricity usage.
I see that you are a newbie, so I would caution you to use your trailer for awhile until you see what you really need based on how you use it before you start making major modifications.