K3500

Is there a way to make this kit just work with an existing door switch? Just to kick off with the SW? If so , how can you do this?

No, unfortunately this will not work for two different reasons:

  1. Kit requires a pulse, not a continuous signal.
  2. Kit pushbutton switches to the (+), while car door switches switch to ground.

How about without the door switch? Can you take the IN to just ground and use the momentary switch to activate the circuit? And can you explain what you mean by pulse?

Most likely this will work as you describe.
Pulse: a momentary operation of e.g. a pushbutton.