That was helpful. The knob idea is not suitable for your abilities. The motion sensor is out.
I understand you want to use your own soft switch and it is designed for that. it's not important that you understand the code, I just wanted it available to you in case you did understand it, or had a local friend that might know about Arduino. Or I suppose, so anyone else that wants one can get one made.
I've never seen or used the automotive beep system in person, only watched a single video where it was described and the video was not clear how the sequence of beeps gets started. Looks like it is by pressing the same switch.
I think the only technical questions I still need answered are the nature of the door opening system, and the mouse.
How do you ordinarily open the door? With a key fob remote transmitter?
If so, we would need to obtain a 2nd transmitter which could also be programmed to open the door. Then interface with it.
Need to know if there is one button for open and a different button for close, or if both operations are handled by a single button.
You want mouse buttons, but not mouse directional control. Those things are usually one device. What is currently providing mouse direction control? your wheelchair joystick? Name the type if you know it. Perhaps Omni 2?
Is the computer mounted on your wheelchair(wired mouse) or laptop always with you(wired or wireless mouse)? 2 mouse beeps early in the sequence.
If it is a desktop computer left at home when you go out, 2 mouse beeps late in the sequence, wireless only.