The better way to do this is buy a higher quality garage door opener that has the features you want. But
OK, well, if you really, really want this...
we'll need to hack the appliance. That's not disallowed by NEC, but it voids the appliance's UL listing, which means it's no longer approved equipment. So it shouldn't be hardwired, it should be cord-and-plug connected.
Now if you look at the unit's wiring diagram on page 33, you see there are 2 lights. Their neutrals are attached to screw 3 and 6 (which are internally wired together), and their hots are attached to screw 11 and 12 (which are also internally wired together).
So, we get a 12 AWG appliance extension cord of appropriate length, whose wires have an appropriate rating (e.g. SJOOW), and we cut it in half in the middle.
For the plug half of the cord, strip the ends and unhook the lights from the sequencer 120VAC board. Wire-nut the cord's black to the light's blue (blue!? This thing won't export to the EU!) and the cord's white to the light's white. Ground to chassis.
For the socket half of the cord, black goes to sequencer board terminal 3, and white goes to sequencer board terminal 12.
If you plug something other than a couple of lights into this socket, you will fry the sequencer board. I wish we were doing this with NEMA L5-20 sockets and plugs so that would be less likely.
So now, the house's wiring. Install, right next to the garage door opener, a common 120V outlet and an inlet in a 2-gang box. Run 2 sets of #12 cable (or better, wires in EMT conduit), with one marked a color at both ends.
- The colored one goes from the inlet to the light switch BOX. You will need to install a box extension providing at least one round "knockout", both for wire space and to accommodate a UL listed (not RU listed) general purpose relay such as a RiB. The two 120V coil wires go to the marked cable we just brought down. The two contact wires go between the switch terminals (paralleling the switch). At this point the garage door remote should turn on all the garage lights. You MUST use the relay. Don't even think about playing wire roulette and trying to find a way to omit the relay: even if it "works for the moment" that would be all kinds of bad.
- The unmarked cable goes to anywhere it's convenient to get switched-hot and neutral from another garage light. This could be a nearby garage light, or it could be the switch.
- You might be tempted to fit only the inlet, and plug the cord into an existing ceiling light recep. My way makes it clear what the inlet is for, so someone doesn't think you just chose a super moronic place for a generator inlet.
Any power applied to the inlet causes the garage lights to turn on. The garage door opener's internal lights are now on an external cord.