I guess these manuals are mediocre and somewhat generic and don't always describe what actually is.
Most likely you have a copy of the Mercruiser owners manual that sometimes comes with the boat when new. This is not a factory service manual and only has limited info about possible equipment installed and limited troubleshooting/service info. Yes, they are limited and really only give the reader info about operating and do cover the entire possible range of equipment available at the time the boat was manufactured. Mercruiser does not manufacture boats, only the engine/drive/controls packages installed by boat manufacturers, Mercruiser has no idea what style tilt/trim system you have, they only list the possible systems based on what they designed for that time period.
If you have the factory service manual it will detail all possible trim/tilt systems, have wiring diagrams, service and troubleshooting information and a very comprehensive breakdown of all the systems.
I am not so sure about the remote. Maybe it was replaced at some point prior to me owning the boat.
The remote you have pictured most definitely was NOT installed at the factory when your boat was manufactured. As I stated earlier that remote did NOT exist in 1988. It is a direct/oem replacement for the original remote that somehow failed.
The buttons on the remote shift lever (see pic in post #15) will move the drive up and down.
That's good. That button is supposed to allow the operator to control the tilt/trim system and according to you it does.
To see if this is the trim/tilt control or the trailer buttons I did the following test. I disconnected the pur/wht connection (see red circle on picture in post #2) and ran the pump again. This time only the DOWN function worked but not the UP.
Again, that's good. By disconnecting the pur/wht wire you eliminated the trim limit switch from the circuit and the button on the remote (which relies on the limit switch to operate up/out) only works moving the drive down. The limit switch mounted on the port side of the gimbal ring completes the circuit for the up trim control until the drive reaches the trim limit. Once trim up limit is achieved the switch opens and the drive ceases to travel up/out. Then the tilt/trailer button is depressed to allow the drive to continue up until maximum height is achieved.
So I came to the conclusion that the buttons on the remote shifter are the trim/tilt control buttons and not the trailer buttons. By disconnecting the trim limiter I simulated that the drive reached its allowed heights dictated by the limiter and stopped. If this had been the trailer controls should the pump not have kept running to push the drive a little higher for trailering? ............There are 2 distinct separate functions, there is the tilt/trim and the trailer. The first is controlled by the limiter switch and the second is controlled by the operator. Now I still have to figure out where the button for the trailer override is.
The button in question from post #15 is indeed the trim (up/down) AND the trailer button. To operate the trim you press the button up or down. In order to operate the tilt/trailer function you simply press the button up harder, as in overcome the first detent in the button allowing it to override the limit switch wiring and tilt the drive completely up.
Trim = drive moves full down and up to the trim limit
Tilt = drive moves up past the trim limit as far up as needed for safe trailering
Again I'm curious as to what your actual question is. You've mentioned multiple times the system works and many here have confirmed the system is in place, is oem, and is working properly. As to your confusion I hope you will carefully read through this entire thread again and come to the conclusion the system is correct