Howdy!
I am not 100% sure of what I did to get this to pair. I can tell you for sure, just pressing the button on the controller for any amount of time near/next to the module in the trunk is not the solution (at least if you're using a used controller).
My guess is you have to clear any prior pairing in the module & the controller. I am only going to go over things I did that made something happen either in the controller or with the car.
One think I noticed very quickly is the (recessed, very small) reset button to the left of the red LED on the module. (Folks in this thread mention that reset button.)
I pressed and held that reset button waiting to see if anything indicated the module was ready to pair - flashing LED, for example.
What happened in my car is the car beeped twice & the trunk light blinked once. So then I thought maybe that cleared the module, so let's try pressing & holding the controller button.
The car beeped again & the trunk light blinked. I thought this meant the units were paired, but when I pressed the button, I did not hear the flaps open.
I pressed the reset button on the module once - nothing. Then twice, quickly - the LED started flashing. This suggested to me the module was in pairing mode. No idea if that was the case or not - but hey, my garage door opener LED flashes when it's ready to pair to the car so, what the hell - mebbe I'm right.
Next, I held the controller near the module & pressed the button. I heard the flaps open. (What I can't remember is how long I held the button down.) Once the flaps opened, the red LED on the module flashed (I know when the flaps are activated, that module LED flashes).
The LED ring on the controller glowed steadily, then faded to off. This suggested to me "successful pairing". Sure enough, now when I pressed the controller button the LED ring on the controller would flash quickly (which indicates it's sending the signal) and then the gates to the seventh level of hell opened, and I shit my britches.
I had no idea that exhaust was that loud.
So I don't know exactly what I did that worked - but I think to pair, you need to press that little reset button.