I purchased ERA #375 in 2003. It was built in December 1992 so was 11 years old and 8500 miles.
Things to look for....
Visually, you need to check all over the body to make sure it is right. Next, I would (before arriving) ask the current owner to have the car up on jackstands when you arrive. I would use a creeper and check the undercarriage to insure that all is right and not damaged.
In the engine compartment... #377 should be about the same age as mine so make sure all hoses and belt are good and supple and new. Check the cooling water and
oil before starting up. ALso the brake fluid reservoir. Should be clear fluid not cloudy.
Visually check the cockpit. Is it clean and tidy? Do the gauges lite up?
Start the engine. It will take the engine a long time to warm up. This is NORMAL. It will sputter and gack and pulstate when very cold. This is NORMAL. After a few minutes of revving to keep it from stalling out it should idle down to a low ticking grumble.
Listen for vibrations in the exhaust pipes.
The proof of the pudding is in driving the car. The trannie and shifter linkage have a long throw in a Toploader. Probably 377 has SW gauges. See if the tach is stable on readout. Mine used to bobble until I fixed the wiring.
To be frank with you, I would suspect that 377 is just a dandy car. I saw pictures of it and it looked super. Make sure there are all the details on the provenance of the engine, trannie and differential.
The previous owner of my car had all his details and records and receipts in 4 big binders. He also had a few scrapbooks on the build details and photos of the car going together.
Find out what spares and extras will come with the car. I have loads of stuff that came with it from the previous owner... find this out.
Good luck... my used ERA has been a great car for me. They make a super product and there are not too many of them around.
Cheers