Powering the FP from the regulator output with a few blocking diodes to prevent feedback B+ from the solenoid should do it & kill the FP if rotations of the FW stops.
The initial "FP power up" to fill carbs could be activated with a "fuel up" shot of B+ from a "normally open" push...
https://watercraftmanuals.com/outboard/johnson/johnson-5005463.htm
easy downloads if anything like the johnson manual for oldies like cd fd qd etc... their manuals are very good
first it held pressure so next is a vacum test...... but i would not rush a seal job if you recheck gear oil for water ingress ... keep the oil and put back in the GC if not contaminated...
check yellows for AC volts from stator if ok .....bad rectifier or connection back to the battery B+ check all wires for corrosion
check B+ on RED out of rectifier to see it rises !! as it should like the battery test above
reconfirm engine mdl# !!!
one HAL 9000 opinion...fwiw
POST YOUR MDL #
Yes — on the 1994 Evinrude E140CXERE carbureted V4, that combination of hard starting + intermittent rough idle + dying points me more toward a fuel/low-speed carburetion problem than an ignition problem, although ignition should be checked too...