Short problem small block

Could be in the ignition switch. A new switch was cheap for my 65 on rockauto. You re-use your key cylinder, and sounds like removing yours is no problem. There is a little tab you push in with a round wire, with the key in a certain position, then it pulls out. Sounds like your tab many be broken, maybe some gorilla tried to remove it wrong. You can get replacements (I did), but best as a set that matches your doors, or take to a locksmith to re-key.