He told me that an error light will come on if the system detects that the button is "stuck".
Also, I doubt it would work to have pin 8 at +12V when the pulse is inactive. That could damage the control module. That's why I'm thinking an extra relay is needed. The output of that timer seems to be either Vcc or ground. What we want is ground or open. I did not see a mode for that in the timer instruction book.
555 timers have been around since I was in school (40 years ago). The output should be used to control some sort of driver and not go directly into something that you don't know anything about. The "clean" approach is to connect 555 output to a relay driver, connect the relay driver to a small relay and then connect the relay contacts in parallel (NO switch) or series (NC switch) with the dashboard switch. Packaging the whole thing and making it not glitch upon power up may require more creativity. That is why I posted a link in that original discussion to a neat unit that already has all of the design kinks worked out. Spend $3 for a finished product that will plug in and work, or spend hours (or more) trying to figure out how to do it from scratch; its your choice.
Here is something really cheap and ready to go except for an enclosure; I have no idea if it really works:
It might require 2 of these, one to push and one to release the button.
If you can't follow the link, try searching for
Generic 12V Delay Timer Switch Adjustable Module 0 to 10 Second NE555