Here's where I disagree with the above posters about leaving windows and vents open and such. First the OP is in a very wet and humid climate. By leaving the windows and vents open, as much moisture is getting into the camper as there is going out. This serves no purpose, except the walls, floors, windows, everything inside the camper, is now a place for condensation to form. If the outside of the camper is wet, damp, humid, the inside will be too. If this is the approach, then why not just leave the door wide open? After all, you're basically doing the same thing as leaving a window or a vent open.... RIGHT? Because if you do, the moisture will come in and settle over everything. If you CAN keep a fan constantly on, circulating the air, then yes, it will "circulate" the moisture in and out, like when camping. But without some force pushing the humidity out,(remember, the OP has no electricity to even suggest running a fan or the furnace)... evaporation alone will not be enough IN A HUMID CLIMATE. The OP has a vastly different problem than just simple human breath or moisture from a shower, or boiling water on the stove. Cracked windows and open vents work very well when the OUTSIDE of the camper is in a dryer climate. But when it's already wet outside, there's no where for moisture to go. It just site and accumulates more and more.
No. Get the camper dried out from the inside by adding heat. The OP may need to crack a few windows or vents so the heat and moisture can escape the windows, this will dry the inside of the camper out. With the heat pushing OUT the windows, the humid moist air outside the camper will not have much of a chance to come back in. Once dried, then the camper should be sealed up. Can moisture get into a closed Tupperware container? No? So if the camper is sealed, provided there are no leaks anywhere, it should remain dry. If anyone has to vent their campers when in storage to keep the moisture from settling inside the camper, the camper has bigger issues somewhere. Mainly, hows that moisture getting IN? A closed container is CLOSED.
I would not get a portable propane burner heater that stands on the end of propane tank. The put out a lot of heat fast, and are dangerous if not used correct. The top of you stove is made to handle a flame, and has all the protection around it and space to prevent something from catching fire. Plus, the stove will put heat in the camper a little slower, allowing for things to to dry bit more naturally. Crack a couple windows after the camper gets nice and warm. When everything in the camper feels dry. Then close the windows tight, turn off the heat, or better yet, reduce the heat slowly. Go back in a couple days and see if you're still dry. Remember though, every time you open the camper door, you're letting humidity back in from the outside.
A sealed container just cannot get wet inside!
That's my best suggesting to get things dried out in the OP's camper. I use the stove top in my camper all the time to produce quick heat, to help suppliment the furnace when first first heating up the camper (especially in the winter) after sitting a while and I need to do something inside, or if we're traveling somewhere, need to get into the camper and feel that dampness in the air. Rather than running the furnace which requires the battery, which requires electricity to keep the battery charged, we simply flip on the stove top for 10 minutes and it dries out the camper, and warms it up. By the time the stove top has already warmed the camper, the heat ducts for the furnace are just beginning to blow warm-hot air, because the duct are so cold under the camper. It takes several minutes to start blowing good heat. The stove top puts the heat in the living space immediately. AND it's safe! Stove tops are meant to be used!