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I would have a family member and/or friend that has had travel trailers inspect the TT with you. Also ask the owner if he has any maintenance records that you can review.
With any used RV one of the most important inspections is for moisture damage, and this requires free access to the roof. Both the exterior and interior should be inspected closely (seams, doors, windows, inside cabinets, outside storage areas, etc.). Remove the inside A/C ceiling grill (couple of screws) and look for any moisture intrusion via the A/C gasket.
If the TT has the original tires, these will have to be replaced, no matter how good the tread looks. The wheel bearings will need to be re-packed along with a brake inspection/adjustment.
Get under the TT and look for any signs of impact that may have taken place (bent frame, leaf spring shackles bent/worn, etc.). Roll out the awning and inspect material.
I would request to see that "all" appliances function properly, in both LP and electric mode were applicable.