I've wondered about this but the receiver acknowledges the signal.
It appears that the problem is not with the sending unit on the bike or the receiving portion of the HD wall unit as you have stated that the LED on the receiver flashes and you hear a click.
I would have to agree that it is either the wire between the HD wall unit and the push button on the wall or the relay in the HD wall unit is not working even though you hear it click.
If you have an ohm meter (you can get a cheap one from Radio Shack for $10 on sale) you can figure it out pretty quick. First disconnect the wires from the wall push button and the HD wall unit. Connect the ohm meter (using the lowest setting)to the terminals of the HD wall unit and flash your high beams. When you hear the unit click you should see the ohm meter needle jump or move toward zero momentarily. That indicates the relay is closing and opening as if you had pushed and released a switch. If the needle doesn't move it's a good bet the relay is bad and you need to replace the HD wall unit.
Next, connect the HD wire to the HD wall unit and connect the ohm meter to the other end of the wire. Flash the high beams again. If the needle moved on the first test but does not move this time then the wire is bad. If the needle does move, your problem may be how you connected the wires to the push button on the wall. They should be connected to the same terminals as the wire that goes to the opener.
When I installed mine, I plugged the HD unit into the outlet in the ceiling that the opener is plugged into and ran the wire to the opener instead of the wall button. You might give this a try if the testing shows every thing is OK and it still doesn't work wired to the push button.
I hope this helps.
Stan
PS You can jury rig a flashlight bulb and battery to use in place of a meter.