I personally would not own a trailer that did not have a built in propane furnace or a
fridge that ran on propane. I would not want to give up the flexibility of being able to camp for days on end without the need for a
generator. Yup I have
solar on my trailer but it doesnt work out to well on overcast days with lots of tree coverage.
Yes one needs to be sure the propane system is inspected regularly (just like your home furnace) and that you have a propane and CO detectors that actually work & that you replace them every few years. Just like the smoke and CO detectors you have in your home. I may have less of a fear about using propane due to having spent my life growing up in homes with either oil, propane or natural gas furnaces. Any combustion system in a home can and will produce CO if not properly maintained and vented just as is the case in an RV.
Having said that and after rereading the OP's original question I admit I would be very reluctant to use a propane furnace that had been in a trailer since 1974 no matter how good it looks & even if I had a CO detector. Just as I would have concerns for my safety and that of my families with running a 40 year old gas furnace in my home.
There are old RV propane furnaces out there that are not safe to use due to rust or lack of adequate venting in their original design & as a result they are no longer made. As a number of old
Boler owners here in BC have discovered there are qualified repair people who will not touch the old furnaces with the poor venting other than to pull them out and replace them with a newer safer designed furnace.
If I was the OP I would as other suggest take the trailer to a qualified/certified party (not the neighbour who has had lots of old trailers he has fixed up) and listen carefully to what they say about the furnace & its safe use.
IMO CO is as they say a silent killer & not something worth taking a risk with just to save a couple of hundred dollars by not buying a newer safer designed furnace.