Submitted for what it is worth. One day I was bored and looking for something to do...
I have a 2-car and a 1-car garage bays. Each bay had one ceramic fixture for one light bulb. Not much light. The ringed florescent bulbs didn't provide much more light and quickly failed.
I bought some of the cheap HD 4' 2-tube florescent lights for my garage and installed two in each bay. After changing out the ceramic fixtures for a 3-prong duplex outlets, the florescent lights simply plug in and are controlled by the same wall switch. Much nicer.
For the remainder of this, I'm only talking about the 2-car bay. I have done nothing more to the 1-car bay.
My 2-car garage door opener only had a 60w bulb (max) and was not very bright when I came home late at night. What to do? What to do?
I noticed that my 2-bay garage door opener and garage lights are on the same circuit breaker---so there is no worry about back-feeding a circuit.

I'll build a relay to parallel my garage wall light switch---using current from garage door opener light bulb socket---to control my garage florescent lights.
Parts list for relay control:
(1) 2P2T 110v 10a relay from Radio Shack.
(1a) Relay socket for above from Radio Shack.
(2) 110v Neon indicator lamp from Radio Shack.
(3) Pigtail, polarized, one 2-prong lamp cord with inline switch from thrift store.
(4) Pigtails, polarized, two 3-prong computer/monitor power cords from thrift store.
(5) Blue 4"x4"x3" old work electrical job box from HD.
(6) Metal cover for above 4"x4" job box from HD.
(7) 1800w solid state photo sensor from HD, the type used to control lamp post lights.
(8) Screw-in polarized 2-prong outlet from HD.
Assembly instructions for relay control:
The relay socket (1a), Neon indicator (2), and photo sensor (7) are mounted through the metal cover (6).
The pigtails (3, 4) enter the job box (5) by three drilled holes and internally knotted for strain relief.
All wiring is soldered inside the job box (5). Job box (5) is screwed to wooden ceiling supports used to mount garage door opener. This places the metal cover (6) on the bottom of the ceiling-mounted job box (5) so the Neon lamp (2) is visible and the photo sensor (7) can see daylight shining through the garage door windows.
The Neon indicator (2) is used as a diagnostic. It lights when current is coming from the garage door opener light bulb socket. It is wired in the circuit before photo sensor (7) so it is always ON when the garage door opener light should be ON.
The screw-in 2-prong outlet (8) is screwed into the garage door opener light bulb socket. It is controlled by the garage door opener and turns OFF five minutes after the garage door is activated (to open or close).
The 2-prong pigtail (3) carries current from the garage door opener light bulb socket into the job box (5) where it controls the coil of relay (1). The inline switch/cord is allowed to hang down from the garage door opener light bulb socket so I can easily reach it to turn off this system. The switch in OFF position will prevent current from getting to coil of the relay (1) and the garage lights will NOT come on by the garage door opener.
Photo sensor (7) is in the 2-prong pigtail (3) circuit and stops current if there is enough light in the garage from the garage door windows. This prevents the garage florescent lights from coming on during daylight hours.
One of the 3-prong pigtails (4) is plugged into the outlet what powers the garage door opener. The other 3-prong pigtail (4) is plugged into one of the garage florescent light outlets. (Yes, I know this is called a suicide cord.) The 110v relay (1) controls the current in this circuit. Remember, I am on the same circuit breaker, so I am not back-feeding this circuit, I'm only jumping around (paralleling) the garage wall light switch. This is safe to do provided polarities are observed---hence the use of polarized plugs and outlets.
One pole of the relay (1) controls the 3-prong pigtail circuit (4) that jumps around (parallels) the garage lights wall switch. Power flows from the ceiling outlet supplying power to the garage door opener, through one relay pole, to one ceiling outlet supplying power to the florescent lights:
outlet (garage door opener) ---> relay (pole) ---> outlet (garage florescent lights).
The other pole of relay (1) is used to make the 2-prong pigtail circuit (3) self-latching by jumping current from the garage door opener light bulb socket around (paralleling) the photo sensor (7). Otherwise, at night the photo sensor (7) would allow current flow to the relay (1) coil to turn on the garage lights, but as soon as the garage florescent lights came on, the photo sensor (7) would shut off the coil current turning off the garage lights. Flashing garage lights would be most annoying.
N.B. My other option was to design the circuit without the photo sensor. But this would cause the garage lights to turn ON always, even during the daytime when the garage door was opened. I can build a smarter circuit than that.
N.B. If you don't have windows in your garage door, it will always be dark inside your garage so the photo sensor is not necessary---because it must always turn on the garage lights. In this case, wire the 2-prong wire (3) directly to the relay (1) coil. Don't use the photo sensor---extra work/expense for zero gain. Don't wire the second pole of the relay (1) to make the self-latching feature---not necessary as the photo sensor is not used. The relay (1) coil wired directly to the garage door opener light is all that is necessary for an always dark garage.
After completing and testing, the 3"x5" card wiring diagram was stuffed inside the job box (5) for future reference.
Just for grins I made a card and pasted it to the front of the job box (5). It says "Welcome Home".
It certainly is nice to come home at night to a dark house with a car load of groceries and have the garage light up brightly as I drive in. Most cheery. I close the garage door, unload the groceries, go inside and close the garage/house door, and 5 minutes later the garage door opener turns off its light, which turns off my garage 2-bay florescent lights. Sweet.
When I leave/return to the house at noon, I marvel that the garage lights DO NOT come on, but the Neon light (2) is on---garage door opener light is commanding ON, but photo sensor (7) says NO. Good boy!
Belt and suspenders final thoughts.
Above design isolates the garage door opener light bulb circuit from the garage lighting circuit and so does not exceed the light bulb rating (60w) for the garage door opener.
The current flow in the relay coil circuit is very low (0.01a), so the (in-garage weather-protected) photo sensor (1800w) should last a very long time.
The current flow in the relay garage lighting circuit is much less than the 10a contact rating, so the relay contacts should last a very long time. (8x40w/110v = ~3a) But if it every becomes necessary to replace it, it is socket mounted.
All connections are polarize, soldered (electrical type), strain relieved, and protected inside job box (5).
But I suppose it is possible that something could fail and I'd come home some night to a dark garage. I suppose, in that case, I could use Gummy's idea for a Y light bulb adapter on my garage door opener light bulb socket---just in case: screw a *60w bulb into one socket, and the 2-prong outlet (8) into the other socket.
*N.B. I've learned that compact florescent light bulbs (CFLs) do not like the shaking of my garage door opener and fail quickly. Rough service filament-type bulbs last much longer.
d.r.a, not dr.a.