if timing is not close to correct with the wiper pointed at the marks, then I would say it needs replacing.
what does the timing light show the timing at when wiper set to where the motor will run?
I had to replace my CDI due to the idle timing retarded 14 Deg when set to the marks on CDI.
others had jacked with all the carb linkages just to get it to idle, WOT was as problem.
and it did not help that they had drilled out the main jets too.
took me a long time to finally get the motor...
charge every night or get a small generator.
or solar panels.
please do not disturb everyone else with your loud noise on the water,
that would also be helpful with your battery drain
the motors were designed to have them in place, so I would put them back.
there are check valves and just plain nipples on those.
good luck knowing how they are routed.
hopefully your manual shows that
My guess it is a S130TXRU if it really is a 1996.
what the heck are puddling hoses
there should be a round decal on the block next to starter with some numbers/letters to help ID it
since it says thermal switch 2, there should be more than one.
you need to make sure you are looking at the proper switch, and test it to make sure the manual is correct.
I have found things wrong in manuals before
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
remove your e mail address from the post above and send Boscoe a Private Mesage
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