1969 Chevy Corvette Won't start with key switch

check the neutral safety switch. you should have starter power into it and out of it while in park. if you have power in and none out then replace it. its been a while since i have worked on one of these and i dont have a schematic to tell you exact wire colors but its usually yellow into neutral safety switch and purple out to the starter

Is there a Neutral safety switch for a standard transmission (4 speed)?

yes indeed and thats probably your culprit, especially on a standard. its located at the clutch pedal. the clutch pedal pushes the switch contact closed which will let it start. its a safety device to ensure the clutch is pushed in so if someone tries to start in gear it doent run anyone over. the starter wire will come from the ignition switch directly to the clutch switch then goes to the starter