OK. Not too surprising considering the switch change.
When I try to start the car the car cranks. When I let go of the keys it starts.
Somehow I missed this part when I replied before.
Could be timing, could be the Ignition 2 wire isn't getting power during start.
To test, clip the voltmeter neg to ground and the positive to brown wire connection at the ballast resitor. When you turn the key it should show low voltage in Run and battery voltage in Start.
If it doesn't show battery voltage in Start, then stick the positive into the bulkhead connector cavity. Keep working back until it does.
To save on battery while doing this testing, disconnect the neutral safety at the starter relay. That way you won't be spinning the starter.