Not all starter solenoids have a plunger that moves a gear to engage the flywheel. Most if not all outboards do not. Their solenoids simply make an electrical connection of two thick cables supplying enough power to spin the starter. The gear engages under centrifugal force.
MerCruisers, specifically SBCs do have a solenoid that uses a magnetic plunger to engage a gear to the flywheel, for starting purposes, not PTT purposes.
Outboard and sterndrive PTT systems use 1 solenoid, 1 solenoids or 2 relays, depending the year. Newer systems tend to use 2 relays. These solenoids or relays make an electrical connection to power the PTT motor.
If your system trims the motor up, regardless of which button you push, you likely have a wiring issue.
