The radio no longer works, most likely it needs a tube. The high beam switch doesn't work.
It loves to stall and leave you stranded. It will start again after it's cooled down. Unfortunately there aren't any mechanics left who worked on these when new.
The car is a 5 window coupe. I got it from the 2nd owner who purchased it in 1956 as a second car. He ended up not driving it; only taking it out of the garage once a year and driving around the field behind his house.
I bought the car in 1992 and did the normal maintenance stuff, brakes, tune up, etc. The ride is unusual but very comfortable. The angle of the gas pedal puts a strain on your ankle on long drives.
It keeps up with modern traffic on the highway, but you have to obey the posted speed limit on turns. No turn signals means using your arm. The heater works well on cool fall days.
Long drives?
You've only put 2000 miles on it in 16 years. How many long drives have you taken in it?
Wow, this sounds like a really fun car! If you're interested, people make those aftermarket turn signal indicators that bolt up to the steering column and are wired into the marker lights. We put one on our 1950 Chevrolet Deluxe. It's fun to imagine driving it on the back roads in the Fall during leaf-viewing season.
Does it still stall when hot? Does it overheat or does the temperature rise before it stalls? I could see if it got really hot, or lost oil pressure, the engine might seize enough to stop, and then start when it cools down.
How's the oil pressure and oil consumption? It sounds as though maybe the condenser in the distributor, or perhaps the coil may be shorting out when it gets hot and then the engine dies from no spark.
If you have a circuit tester, you can test the leads of the coil after it stalls and see what kind of resistance reading there is. Also, on a car this old, it could be that the insulation on a wire has worn through, and maybe when the wire heats up from engine heat, it touches something and shorts out.
Pushing it up to 65 mph might be asking a bit much from this car, though. You could get an idea of the problem if it stalls after a certain time, or certain miles, at certain speeds.
In addition to comments in comment 2 you might look to see if someone has rerouted the fuel line over the years. If so it may have been routed to close to the exhaust or other heat source it could case the fuel in the line to "vapor lock" or develop a pocket of fuel in a gas state. Old cars then have a bit of a problem sucking fuel from the tank as a result of that pocket. If you live in a warm climate vapor lock is more apt to happen. I had a 50 Plymouth in the 70's that I had to wrap the fuel line with an insulating material to keep it from happening.
I had a Chrysler Traveler coupe, blue, with fluid drive from about 1951 to about 1954. disposed of because I couldn't keep fluid in the fluid drive (needed seal repair and did not know how to do it) and also because I couldn't then afford its gas mileage, 9 mph in country driving, as I recall. I have never seen another coupe, but great style. What color is yours? I wonder if it is the same one, must be really rare now.
I just finished restoring my 5 window Traveler Coupe, about 2 months ago. We love it, I'm not too fond of the brakes though, they do the job.
It does sound like your car has vapor lock. I rerouted my fuel line way away from the exhaust manifold. We have been searching the web trying to find some more Traveler Coupes. They are very rare. We did add a aftermarket turn signal switch to it it works great.
I would be interested in getting a hold of or talking to anyone who owns one or has owned one. You can reach me at mybadfish@gmail.com