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When I bought mine (from a Chevy dealer) I made it clear that although the car was what I was looking for, right year, right color, etc. that I was also considering several others from private owners. And I also told them what I could buy similar cars for and that I wouldn't give them anywhere near their asking price. I first looked at it on a Saturday afternoon and later, during the week, the salesman insisted that I take it home overnight, knowing that I was a professional tech and would examine the car fully. I did of course and the following Saturday when they finally accepted my offer and I drove it off of the lot, I got it for $12K. Their original asking price? $16K. It pays to go in fully informed, never act anxious or as if it is the only car like it on the planet and let them know up front that you're not BSing them and that you won't tolerate any BS either. Actually my salesman was a pretty good guy. He was a long time Corvette owner and has since retired. Until he did though, I used to stop in regularly and he'd want to know what I'd done to the car lately and we'd just talk Vettes and BS for a while.
Letting a buyer take a car home is a practiced move for a dealer. I did it all the time and it worked 100% of the time.
Its good for both the buyer and the dealer. Once you have the car in your driveway its like you own it. It also gives as you said a real chance to test it out completely.
Most dealers are not in bidness to rob the public. If they were they would be out of bidness in a hurry. One has to take into account that a good profit on a used car is around $1k. Theres not a lot of room with such a small profit margin.
Dealers can offer fianacing, extended warranties, and repair services.
I rarely buy from a private party, last three cars Ive bought were from the dealer. The dealers have the better cars for sale and they can hook you up with the right loan.
I always buy the extended warranty. A warranty on the average is $1200.
The 84 Corvette in question had a weak battery comon for a used car that sits for extended periods of time.