Ideally you'd get ab obd2 reader and check for any pending or historical codes. Also check under the car for rust levels. Sniff test for any mold smells, look for any signs of water inside. Check tires, do the shock absorption tests. Listen when revving the engine for any "odd noises" or bogging down sort of noises.

Best thing is if all that looks good, ask to take it to a local mechanic and pay them to do an thorough check of the car - what's worn, what's broken, will it pass any state checks etc. Expect to pay for an hour of labor.

If they balk I'd be really leery of buying - Wonder what they want to hide.