When I was last shopping popups, my target weight was 2000 pounds, which meant 8 and maybe 10 foot boxes with limited equipment: cold water, ice box or ice chest instead of fridge, no furnace. Many early models (family had one in the late 60s) were like that, even the larger sizes, but 1980s you'll find more are better equipped and thus heavier.
Safe? Safe to tow, in good condition. As safe as a tent for sleeping, if you follow tent safety protocol, no fires inside. No safer than typical low cost family tents with respect to severe weather, i.e. I would be running for shelter in thunderstorms.
Condition is what is most important. You want to find a sound box and bunk ends, well kept chassis, good wheels, bearings, brakes, recent vintage tires, no cracks or breakes in the frame. Wiring, electrical equipment, plumbing (water, and especially LPG) plumbing has to be checked for function, absence of leaks.
To use it, you'll need a tent in good conditon, including screens and zippers, which tend to 'age' faster than the tent material. My tent experience goes back 40+ years, the canvas era, so I look for tears, mildew damage, condition of waterproofing. I'm not familiar with aging of vinyl or vinyl-coated tents, which start to show up in age range you are looking at, but I think I would be wary of any cracking.
Folding, rather than popup, tent trailers tend to be much lighter. Livin Lite still makes them, but the are fairly expensive. I don't know who might have been making them 20-30-40 years ago, I remember them from catalog stores 55-60 years ago, as well as DIY projects. The category is much older than popups, I've seen tent trailer designs from the 1920s and 30s.
I think 2000 pounds is probably a good target weight for towing with a Pilot, but I thought the maximum tow rating, certainly 2008 and earlier, was more like 3500. Maybe Honda lowered in later years?
