Starter issue and leaky primer solenoid

[tsubaki]

I'd check the battery with a load tester to insure it's output capability, then make sure the connections were clean and tight, then check the battery cable for proper size and connections for any problems, even to the extent of bypassing it and using another source.
Had a 90 horse that would not engage but everything else told me it was fine, ended up being a partial break in the cable just as it exited the motor. Had a 70 horse that had a bad terminal eye solder at the battery connection, did the same thing. In both these instances it was low voltage/low current capability.
If everything else fails and tells you it's correct, then look at the solenoid for replacement, then the starter.
Many times the starters and trim unit pumps can be disassembled, blown with an air hose to remove accumulated debris, reassembled and they will work for several years before needing replacing.
Look at the air intake cover, the decals shows the correct positions for the choke/primer operation. Seems like all the way forward was choke/prime and all the way back was normal run. But I can't remember.