I am sure with all the wiz bangs and whirly gigs on my TV it has one heck of a phantom load. It even warns me when the battery is low and shuts off some of the "ignition off" features.
Solar seems like a good plan if the the battery drain and solar panels are small enough and the panels can be placed in the sun when the TT is in the shade.
At this point we are testing the waters and can get by with just an extra battery for 2 or 3 days at the non-electric events we attend.
I have an LP detector that just alarms, it is not connected to a shut off system.