Full Size Jeep Network

I'll put this here for convenience, in case you want to compare the table to the drawing.

I eventually got it working the way I want by modifying the tailgate switch connection and trying to be a little creative : now both the dashboard switch, and the tailgate switch, operate the 2 relays situated under the hood. And I like this solution better than 3 relays.

To achieve that :
I ran 3 more wires directly from the battery to the tailgate that will be 3 ground wires.
The problem was the 12V contant power going to the switch. Well, let's get rid of it. I removed the constant 12V to the tailgate switch and replaced it with a first ground connection.
The 2 other wires connect the brown and tan wires from the switch to pin 85 (one for each relay), just as the dashboard switch is.
This way, either switch completes the circuit and activates the relays, which then powers directly the motor through pin 30.
No power pass through the tailgate switch, which may also be a good thing as it might extend its life a bit.
And I prefer to have the relays under the hood rather than in the tailgate.
Firtly because relays lying at the bottom of the tailgate might get more moisture overtime, and the space available is tight to secure a free route for the window to move up and down.
Plus if one relay fails, there is no need to go into the tailgate again to fix thing, just replace the relay under the hood.
I secured the passage of the wires throught the tailgate hole the best I could with several layers of heatsink inside a flexible sheath.
Things should last a few more years.

So everything works with only 2 relays. More simple and slick design, less prompt to failure I think. Up and down are a lot quicker and feel stronger than they used to be.
I took the occasion to lubricate everything with WD40.
Thank you guys for your replies, especially tgreese for his very thorough explanations.
It certainly helped me a lot understanding how all this trickery works ! (let's face it : what a bad design to start with ! anyway...)
I hope all this will be useful to someone else.

Thanks, and glad it is working good.