Ayuh,..... Those are the idle relief ports,.....
The exhaust, 'n water run together before that, but depending on the lean of the boat, they can separate in the ports like you saw,.....
Ayuh,..... Yer chasing a ghost,..... yer symptoms don't come anywhere near that switch being the problem,....
Quit throwin' parts at it, 'n Diagnose the problem,......
Ayuh,...... With a multimeter, it's an open circuit at rest, 'n closed circuit when the lever is depressed,.....
They usually don't go bad, til some unknowing sole messes with 'em,.....
'n usually when the motor dies when shifting, 'n it's always the lower shift cable most of the times,....
Ayuh,..... There used to be only 3 options,....
With electronic motors, they keep adding more, 'n more sensors,......
Also, be sure the wiring for the sensors are clean, secure, 'n pass current properly,.....
Ayuh,.... To many variables,... If the motor will drag on the ground if left down, of course, that's not an option,....
If ya tow with it tilted, Yes, it's gotta be secured in that position, with whatever works in yer situation,.....
Ayuh,..... But, they come with 2 different filter thread pitches,.....
Mercruiser, 'n Volvo,......
The one you posted doesn't say,....
The Merc housing uses a Napa 3225, or 3226 filter,.....
Ayuh,..... Welcome Aboard,.... A leak down test is done by bringing each cylinder to it's Tdc, 'n blowin' compressed air in through the spark plug hole,.....
If you hear the air through the carb, it's an intake valve,.....
If you hear the air from the exhaust, it's an exhaust valve...
Ayuh,..... That can happen,......
Instead of Teein' the line, install a Merc pattern canister fuel filter, 'n use it's second "out" port,.....
That way, both motors are fed cleaner fuel,....