Yes, absolutely!. You can do this by pulling out the switch, and splicing together the two wires that formerly went to the switch. Then put a blank cover plate over that switch's electrical box.
You should know however, that you don't have to have a constant power outlet for a garage door opener. You can have a garage door opener on a switched outlet just fine. And you can use that switch as a lightweight form of security lockout.
I would recommend instead you put a switch guard like this over it, and just keep that switch on forever. It's less work and easier to undo. It also would let you cut power to your opener if you wanted to without getting up on a ladder.
Put a descriptive label on it "Garage door, do not turn off" if you want.
You can also get adapters that give you two outlets and a light socket with a pullchain, into which you can plug your garage door.
This way you can keep the light in place and also avoid having to do any wiring in the ceiling. However, you should shop around and make sure it can supply the amperage you want. Use LED bulbs to conserve amperage and stand up to the vibration of the opener better.
If you cant find a double-outlet-plus-pullchain-light adapter (above) that satisfies your amperage need, then consider one of the single-outlet adapters:
Lastly, if none of those do what you like, you should replace the light fixture with one that has its own built in outlet, so that you don't lose the overhead light capability. This is rated for the full 15A of a normal outlet, and accepts a grounded plug without the cheater adapter you would otherwise need for the light-socket-to-outlet adapters above.
You can get all of these parts at any common home center. Have fun!
From your description the wiring is normal not "jerry rigged". You can add a new wire to the switch but from the wire count you may not be able to fit everything back in the box and your wire fill would exceed code. It may be better to purchase a 2 gang old work box cut the hole the right size for the box pull the old box and install the new 2 gang box. It may be easier to add a 4x4 box in the attic to make your connections to the outside lights and new feed from the 2nd switch. All connections need to be in a box. The 3 sets of wires in the original switch box are possibly the hot feed, the switched feed to the lights and a hot feed to outlets on the wall this would have been a normal setup a few years back. Remember to turn the power off prior to doing the wiring changes and good luck.
Best Answer
You definitely should have a on/off switch for your security light. I would recommend opening up the wall outlet box and tapping off the 'hot' feed to that box. The simplest way to go is to replace that box with a box large enough to hold the existing outlet and the switch for the security light. Wire the hot feed and the neutral lines to the switch (and of course tie green grounds everywhere), then run a line from the output of the switch to the box (you need an electrical box behind the new light) holding the security light.
If you want that on/off switch to be somewhere else in the house, then of course a lot more wiring's going to have to be pulled.