I picked up a 1973 Evinrude with a donor. I hooked up the battery, turned the "key" (screwdriver), it cranked and then stopped. For a while I could get the choke solenoid to move.
Fast forward. i swapped around a few parts, new battery terminals, etc. I can get the starter to crank the motor with a starter switch (via the relay).
I can't get the starter to crank via the control unit. It seems as if power isn't getting from the control unit to the motor. Earlier I was able to at least get the choke solenoid to move - now noting. I have battery voltage to the relay.
My guess is the safety switch is not set correctly or malfunctioning.
There is a safety switch on the motor that will not let the motor get power if it thinks the warm up throttle lever is set at too high an RPM. Also, there is a neutral safety switch in the control box. Either can be causing your problem. I have your exact motor.