A new cylinder and key does not change the contacts in switch. So you didn't get a new switch. The difference in design is as I said earlier. The old switches do not have continuity between the "Ign" terminal and the "Start" terminal. The newer switches do. That means on an older switch if you hook the HEI to the Start terminal, it would start then shut off when you let go. If you hooked the HEI to the run terminal it would not start unless you pushed the truck. Old design and new design. The wiring you show looks like you have an older switch.
Looks like they have it correct. They have it wired for the case I mentioned. An old ignition switch where run is not connected to start when switch is in start position. The violet wire to solenoid "S" terminal is from the ignition switch "start" terminal. The pink is from the ignition "ON" to HEI and the yellow is from the solenoid "R" terminal to HEI. They are connected together so that HEI gets 12V while starting and while running. If you ever get a new switch, you won't need yellow from "R".
If you have a separate issue with spits and sputter, I suggest another post.
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