Best I can tell,
the start switch, when turned to the start position sends power to the thermal switch 2 with the brown wire .
if the Thermal switch/motor is cold/closed it heads to the choke solenoid
look this up online.
YAMAHA OEM OUTBOARD SERVICE MANUAL LIT-18616-01-97
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only oil sensor on that motor I know about is the float switch in oil tank, and no linkage is hooked to it.
the oil pump does have a link to the throttle so it can change the output of the pumps as throttle goes open for higher RPM
1st ,did you put in a kit or just the new impellor?
was the housing still good?
I would try running the motor in a tub of water or on muffs and blow some compressed air up the tell tail hole to see if that moves something out of the way
if the primer bulb can suck and pushes fuel from the tank to the motor ,
but the fuel pump cannot, there has to be a problem with the pump or a connection between the primer bulb and motor
copression test, and then use a timing light to see if each cylinder is sparking at the correct time.
if no good spark on one or more cylinders, measure the peak voltages into and out of the CDI
I see it has a charge coil and Lighting coils, but the pulser coils signals to tell when to spark...
guessing at what is causing the alarm is no good,
and running the motor with the alarm sounding for 45 minutes is a bad Idea. what do your gauges tell you is happening when the alarm sounds?
is there a switch that operates the solenoid or maybe pushing in on the key switch would operate the solenoid?
are there butterfly plates in the front of each carb that the linkage is tied to?
if so what operates those.
they should not be closed when running
can you run the boat with the cowling and silencer off so you can see what all is moving and opening/or not opening as you open the throttle when the problem shows up.
something is affecting all 4 carbs /cylinders
so what does the solenoid do?
is it connected to all 4 carbs?
what does that linkage attach to and move?
almost looks like a choke plates in the front of carbs.
and the linkage in the parts breakdown call the linkage choke linkage.
is it possible those are not opening back up like they should?
pull the stat and test in a pot of water as you heat it up, make sure it opens according to spec.
The only other thing that I can think of that could affect fuel to all Cylinders would be the prime start enrichment system.
make sure it is allowing the extra fuel when motor is cold and then...