Inspect the end of the ignition switch connector..
Make sure that none of the terminals have burned or backed out of the connector body..
Did you put a new ignition switch on the side of the column.. ?? like this: https://bit.ly/2TCphD3
look at picture 2.. see the slot where the control wire goes in.. you can push the switch in one direction and look inside at the contacts .. see if they are burned on one edge.. meaning that somebody put a old switch back in the box and returned it to the store.
lets do a test.. do you have a test light.. unplug the S terminal on the starter solenoid so you are not cranking the engine.. find the coil positive connector.. it will have a second short pigtail to the external capacitor.. stick the probe in the positive side.. ground the test clip.. slowly turn the key from the locked position thru run.. thru cranking .. slowly back to run... then slowly back to locked.. you should have constant power with no flickering from Run, thru cranking and back thru run till you get to the off position before you get to locked..
Another test. turn the key to the On position.. the test light is still hooked up in the coil positive... have a friend watch the test light. while you tug on the ignition switch pigtail.. i had one decades ago. .that the pigtail was not snapped fully into place.. it would die when drove the pickup up a steep hill.. drove the owner crazy.. drove the dealer crazy. they finally called me and i found the connector not snapped in fully..
You can see that the pigtails come out of the ignition switch connector really easily: https://bit.ly/3giiI2c
This is a quick test.. probably less than 10 minutes.