Greetings Trout Fishin!
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The '78 Ambassador that you are looking at has an empty weight of 4,630 pounds with a hitch weight of 550 pounds (twin bed floorplan) or 575 pounds (double bed floorplan). You can find this information at:
Airstream Weights and Measures
These weight are both empty and each will increase significantly once the trailer is prepped for a vacation trip. What empty means is that none of the installed options are included in the figures nor are any fluids such as water or propane included in these figures - - the holding tank(s) are also empty.
To give you an idea of what loaded weight might look like, my '64 Overlander has an empty weight (with all installed options) of 4,440 pounds with a hitch weight of 475 pounds - - when it is fully loaded ready for a vacation, the coach approaches 6,000 pounds with a hitch weight approaching 750 pounds.
I suspect that your Explorer would be maxed out on its trailer towing capacity if not in excess of its rated capacity. Another issue to consider is the diparity between the wheelbase/length of the tow vehcile compared to the length of the trailer - - the greater this disparity, the higher the probability of an uncomfortable towing experience; and this can be compounded in circumstances where the trailer is significantly higher than the tow vehicle. If I were looking at a trailer of this size, my preference would be to have a tow vehicle with a trailer tow rating of at least 7,200 pounds to allow for a margin of safety (IMHO).
The price at which the trailer is being offered is very attractive. If it is truly fully functional so far as the interior components are concerned, it MAY be a very good buy. The length of time that the coach has been setting would indicate that the following may be issues that will need to be addressed:
1.) The tires will be a near certain replacement item.
2.) The bearings and brakes will need to be serviced before any serious towing is considered.
3.) If the trailer has the optional(?) vacuum over hydraulic disc brake system, they will likely need service to be functional; and there are two chanins of thought on whether it is better to overhaul these units or replace with the more readily available electric drum brakes.
4.) The axles may have taken a "set" during this extended period of inactivity which MAY result in a fast road to replacement requirements.
5.) The propane tanks will likely need to have their valves replaced with the currently required OPD valves - - not an excessively expensive modificatgion, but may be time consuming in trying to locate the valves for aluminum tanks if the coach is so equipped.
Even with those four issues involved, if the interior appliances are functional, the exterior skin is in good condition, the floor is sound, and there is no evidence of unrepaired rear end separation or droop ; the price may very well be within reason.
Good luck with your decision!