Funny how?
It doesn't amuse me.

It's slow to react.
When I press either of the three buttons that would lower the starboard drive, it takes a few seconds for it to kick in.

Up is instant.
When I press the single button on the dash to lower that drive, it takes several seconds before the pump kicks on.
When I press the 'both' button on the throttle or dash, often the port drive will go all the way down before the starboard starts to move down.

I'm suspecting a corrosion issue, and either it needs to 'heat-up' the amps to get through the corrosion to get the solenoid to move...
...or perhaps (another) solenoid going bad.

Thoughts?
Where to start troubleshooting? Behind dash or trim pump connections?

Or is this something else?
Fluid levels are fine and still look like new oil, but fluids could probably used changed due to age.

Thanks in advance.

Swap the up and down feed wires at the solenoids and see if problem is same. If same symptoms solenoid motor/problem, if it follows the wires then dash/wiring problem.
Then you could swap the solenoids to verify if solenoid or motor is problem.