So sorry to have disturbed you.
You certainly didn't disturb me per se, it's just that we see so many people asking obvious questions when a cursory look at the ON LINE manual would factually answer their question "according to the manufacturer's instructions."
Pretty obvious where and what the computer is with a glance at page iii. Your chartplotter doesn't have the software to read the ST 4000+ input and then compute an output to the servo motor at the wheel. Only the ST 4000+ control unit can do that. The control unit is the computer to which you refer.
As for the compass, that's more than a bit of a bugger. Mine is buried at the very bottom of a hanging locker against the forward edge and you do have to look closely to find it. All I can suggest is a closed off space in the middle. I don't even want to say this but maybe take a look in the bilge for an elevated surface.
After working on a repair job on my ST 4000+, I learned that it is a fairly old model autopilot for a 2016 boat. There are several newer models since my 1999 model Autohelm ST 4000+ model in my 1999 new boat from he factory. If you are the second owner of the boat, there is a possibility that the previous owner may have got his hands on an a second hand 4000+ and installed it. Not knocking the 4000+ for a split second here. Have had mine for 24 years and flawless performance. Did a minor rebuild of a couple of broken posts in the drive unit last year and it still performs flawlessly. Several people here have described the older 4000+ model as superior construction compared to the newer units.
What I'm getting at with reference to a previous owner having installed the unit, you could be looking ANYWHERE on your boat for the location of the compass and not according to the manufacturer's instructions of near centre. Any chance of getting down and dirty and getting behind the control unit and tracing the wire leading to the compass :
................. as a last resort ? Good luck.