It sounds as if you need the 3034-P adapter, rather than the 3036-P that you have. Sorry I made the mistake of confirming the 3036-P in my post #2.
Link to buying a 3034-P is here
. On that page is this comment:
The 3034-P cable was the correct cable to interface the Tekonsha P3 Brake Controller with my 2018 Jayco Class C 29MV on a Ford E-450 Superduty Chassis. I verified this with the techs at Tekonsha. The previously ordered 3036-P cable did NOT work. When connected the RV would crank but would not start, and the P3 had no indication of power. The 3034-P cable did the trick. The RV starts, the P3 has power, and after a test drive today I can report the P3 is activating my trailer brakes properly.
You can also re-pin the 3036-P you have to match the 3034-P. You release the wires by removing the red retainer. Then you can get the pins out, best with a pin removal tool, but sometimes with a very small screwdriver, like one used for electronics. Re-pin to match the 3034-P pictures shown at the link above. Reinsert the red retainer. Done.
Easier to order the 3034-P overnight delivery, though more expensive.