First, have you used an oven thermometer to check and make sure the unit is reaching full temp ? If you set on 350, do you get 350 heat ? Is it slower to heat up than normal ?

Otherwise....Three choices.....you (or a variety of people) have enjoyed +50 years of use of an appliance from the golden age of appliance design and manufacturing. Give it up and buy one of the new models which won't last 1/10 as long before it needs major surgery. Since you are on this forum, I know you already discarded that concept and are willing to save your classic oven.

Find an 80 year old technician who knows how to work on the old style circuits with relays.

Do it yourself.....and here you are..

A relay for the top element has failed. The relays are electromechanical switches that go on/off based on an input signal.

The broil relay is a different switch than the bake relay controlling the same upper heating element. Without a schematic it will be something of a challenge to isolate and troubleshoot, it can be done.

First, DISCONNECT POWER SUPPLY....usually at home power panel.
Second CHECK TO MAKE SURE POWER SUPPLY IS DISCONNECTED
Third VERIFY POWER SUPPLY IS DISCONNECTED

Be careful, your oven could have two power feeds. Since it is a 50's era oven, you could have a 50's era power panel in your home with older style screw in fuses or even the cartridge type fuses.

Remove cover panel and oven from wall, and see if you can trace wire(s) from broil element back to relay(s)...(usually a metal encased 1inch cubed on the sides item)

Could be as many as four relays in the control area. I doubt you have self clean option....
Broil Low - puts low voltage which generates low heat across the element
Broil High - puts high voltage across the element for high heat
Bake Low - you get the idea
Bake High

If you are real lucky, the control board is well labeled. They used to do that.

The tricky part is confirming the relay is bad. Some relays are 120volt input signal, some are 12volt. Should be labeled in some way. The relays are all Normally Open, and need an input line voltage to close the switch. Usually easy to hear them CLICK as the switch activates against the spring. If you have the right set up , you can apply a voltage to the input poles and check the continuity across the switch. more than likely , the contacts are just burned up. And yes, they can be replaced.

Some relays are plug in modules. If the broil high/low are same footprint, swap them and see if oven works on bake as desired.

Your choices are then find a replacement relay or live without a high setting on broil while you find some one who can repair/replace your relay.

Good luck and let us know how your restoration project goes.

The good news is you don't need an exact replacement module. You just need something with a similar rating for input signal and line load to match. Relays are still VERY commonly used.

You might have to solder on some quick connect female ends for the various wires to slip onto the male posts on the newer relay

If you are real lucky, there is no soldering involved, and it is literally a matter of connecting up a new relay like wiring in a new outlet. I would be surprised if they still sell relays with screw down connectors. They have almost all been replaced with slip on quick connectors.

The line rating is likely to be 208-240V at least 30amps.

The signal rating is the unknown...if you have a transformer inside it is likely to mean the signal line is a 5v or 12v DC. The way to trace the relay could also be off the control knob (or push buttons). Just follow the wires from the right position off the knob/button as the signal wire to the relay it controls.

If you are in a larger metro area, there is probably a WW Grainger industrial supply which sells every motor control (common use of relays) components and they can help you find a replacement.

Good luck again.