Ok, based on what you told me about the car and without having seen any pics, here is what I suggest you do when you go to look at the car.
Since its a US based car, the first thing is to ask to see any documentation he has. If the car was restored, he most likely will have found and removed the tank sticker for safe keeping, especially for a car of that pedigree. If there is no documentation or history, you cannot assume it is the real deal. Take pictures of everything in case you want to pursue. Start by checking overall condition as Tyho and Tourmax suggested, even though it is restored.
If you like the look and state of the car and want to check for clues that car is really what the owner claims, here are the basic checks you can perform yourself.
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Start by checking the Trim tag, yours should be similar to this example of Black/Red 435hp car which I found on the internet. J22 at the top is car build date. Letters are assigned starting with 'A' for Aug 66 (first month of production), B-Sept, etc. J22 means this car was built May 22, 1967. Take note of the date so you can compare against casting dates and build dates on engine to see if they make sense.
Trim 408 indicates Red leather interior, or you may have 407 for Red vinyl.
Paint code should be 900 Tuxedo Black. That will confirm that you have the correct paint and trim colors.
Serial number is on ID tag on the right, this example was 19139 of 22940 built in 1967.
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Next, you look at the stamping on the engine pad. The number on the right is the car serial number which should match the serial number on the ID tag. The code on the left is the engine build date and code. ‘T’ indicates built in Tonawanda factory (all big blocks are ‘T’), 0510 indicates build engine was assembled May 10, and JE is the code of 427-435 hp. In this example, the engine build code seems ok for a car build date of May 22. Yours should also have JE code, and engine build should be approx. 2-4 weeks prior to car build date as you determined from trim tag (although some exceptions are known).
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Now you look at the engine block casting p/n. It is located at the back of the engine, driver side where it mates with the bell housing. It should read 3904351. At the same location on passenger side, you should see a 'HI PERF' marking. There is also a casting date you should check. You need to crawl under the car on the passenger side. The date code will be just above the oil pan lip near the center of the block, Month –day-year, where letter ‘A’ is Jan through ‘L’ Dec. This picture is not from the same example as above and cast date is Jan 24 1967, which would be too early for a May 10 engine build. I your case, casting date can be up to 2 months prior to engine build date that you determined from the previous step. Look at all the dates you have established, they should be sequenced by casting date first, then engine build, then car build. Keep in mind, none of this ‘guarantees’ that the engine was original to the car, or that the car was originally a 427. But if it doesn’t match or dates do not line up, it’s a sure sign that it’s not real.
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There are a few other obvious easy things to check, Oil Pressure gauge should be 80 psi, Tachometer redline should be 6500.
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Also, all big block cars came with factory rear stabilizer (sway) bar which bolts on to the rear trailing arms on either side just behind the brake calipers.
At this point, if you are satisfied and everything seems good, you have some decisions to make. If you are interested in buying the car only if its the real thing, then I strongly recommend the next step would be to hire someone qualified to have a deep dive look at the car, especially if the deal is too good to be true. Keep in mind, 67 Conv. Black with Red interior 427-435 is the 'mother' of desirable Corvettes and usually priced accordingly. No matter where the car is in the US, there are local chapters of NCRS that will gladly recommend someone for you. On the other hand, if you don't care, you love the car and just want a beautiful car to drive and the price or trade is right, then you found the perfect car.
Good Luck, keep us posted, and yes.. share some pics!