Reducing voltage in a 1966 AM car radio
You could try a regulator such as the LT1084CP-12#PBF. It is a fixed 12V output regulator in a TO-247 package, good for up to 5A (60W out). They're about $13 each. 



The inverse diode across the regulator is probably not necessary, but for a few cents, is not worth eliminating. 



If the voltage drops to less than 13V or so, the output voltage to the radio will also drop. When the car engine is not running, the voltage on the electrical system is normally only a bit over 12V, so you won't likely get more than 11 and change at the radio. 

If you have a adjustable bench DC power supply capable of enough current you could change the voltage downward from 12V and verify where it stops working. You could also verify the current draw to ensure that 5A is sufficient.  

You must have a sufficiently large capacitor of the correct type on the output of this kind of regulator (it's an LDO type) or it will be unstable, I suggest a normal (not low impedance) 470uF/25V electrolytic rated at 105°C. I do not suggest a tantalum or ceramic part. A similar part on the input will be okay. They're about 45 cents each. 



I would also suggest a healthy unipolar TVS diode on the input capable of 1500W surges and rated at perhaps 24V. Something like a 1.5KE30A-TP. about 50 cents. 



Be sure to provide a sufficient heatsink.. a 5A load with 3V drop means 15W are going to have to be dissipated without it getting overly toasty, even on a fine summer day with the dash really, really hot. The part has thermal shutdown to save itself, but you should not test it.