Welcome to the forums, glad to see another NC person on here. I can think of quite few things that need to be checked on the LP. Spiders love the smell of LP and build webs/nests in places like water heater vents and furnace flues. Not sure about the 1968
but in the early 70's vintage there are a lot of parts to check out, every appliance has a shut off valve, you have the actual connections to the appliances and the appliances themselves. If the system has not been used in a few years I would expect at the very least to have to clean some burners and check for cobwebs, I would also get some fluid from your friendly HVAC/appliance dealer to check for connection leaks. The good news is that the LP system is exposed on the under side of the trailer (by code) and fairly easy to replace. I would consider replacement anyway. If the trailer still has the OEM system you are looking at 40+ year old copper tubing, fittings and rubber hoses that have been wandering down the road, and being exposed to all kinds of things.