I want to recreate this existing ALPS switch board (the board on the left) in Arduino, so I can control the switches (and 3 memory + 1 menu buttons) from my laptop. The ALPS switch board connects to a controller board (PSM) with relays, microprocessor, and DC motors connected to it.

The idea is to use Arduino to completely replace the ALPS switch board, while still preserving the controller board connection and current wiring and connector (16 pins + 2 empty pins).
Is there a way I can just connect the 16-pin connector directly to header pins on a certain Arduino variant? And program the individual pins, to replicate the manual switch input + 4 buttons?
See pin diagram attached (seen from the other end of the wiring, on the controller board side), where I get a little bit confused about terminal #C4 - #C7.
If easily possible, I want to use the controller board power, not the Arduino power. I’m also not sure about what the 2000 Ohm resistor on the left side does exactly.
Edit 1: Hopefully the new picture above clears things up a bit. The switch board connects to a PSM (Power Seat Module), which controls the DC motors of an early 2000s car power seat (don't think the OEM matters here). I want to control the PSM with my Arduino (so I don't have to use the ALPS board anymore). In other words, I have to replicate all the functionality from the ALPS board with my Arduino.
Edit 2: A picture of underside of Alps board:

Edit 3: The P/N for the switch board is: ALPS ANJ971038D RH DR. And for the PSM (which includes the relays): ALPS ANV971018A. There is no public documentation that I found for any of the 2 boards. The pinout diagram above is from the dealership, but I'm not allowed to post further details about it.
Here are the results of what I measured myself using my multimeter. When the switch board is powered from the PSM I measured 4,5V on the + and - of the 4 memory buttons in neutral position. By pressing a memory butting the voltage drops to 0V. The + and - on the white switches measured 11,90V in neutral position. According to the pinout diagram the voltage is supposed to drop to 0V, but this didn't happen when I moved the switch while measuring. I also measured a resistance of 1490 Ohm between pin 2 and 5 of a white switch (so the neutral position), while the switch board was being powered! No resistance when the board is disconnected from the PSM.
I also measured pin #C4 and #C6/7 right from the connector, and I got 0,99V. #C5 and #C6-7 gave me 2,95V. Pin #C4 and #C5 are connected to the resistor (R1).
The switches are all momentary switches.

