I guess the question is, can you simply ground the parking brake wire and it work? Or does it require a delay or other trick?
First test, if no one has info on that head unit, would be to ground the parking brake wire and see if that works after turning it off / on. Might be that simple. And or then grounding it after power on to see if that makes it work. I did a quick look at the manual and it showed it needed a ground signal, assuming I was looking at the correct manual.
I recently made one up with spare parts for an older Pioneer DVD head unit I put in my truck. The Pioneer needed a “delay” on the parking brake wire at boot up, so just a relay won’t work, and I did not want to use a toggle switch to manually do it. I did about 10 seconds after turn on, then the relay kicks on grounding the parking brake wire. I had tons of spare parts from doing electronics repair, so already had crap to play with and make work, but busted out the breadboard and box of old parts to tinker, didn't need any precision timing. Not really worth playing with though if I had to buy parts, I'd just buy the correct bypass module and be done with it. The Pioneer didn't need anything special, I had parts I could make work, so in my case it didn't hurt to experiment, and it is a beat up truck I use to haul crap, so I wasn't about to spend the money on a bypass module if I could get around that.