I recently did a short where I thought a blinking red light (see "Wired") might look good on an electrical control panel. But I couldn't just trip the system or set off an alarm -- my employer might not look approvingly on such actions. I figured I could probably fake it in Final Cut Pro and save myself some hassle.
This tip will work easiest on a stationary shot.
STEP ONE: Add a video track on top of your shot. This is where your blinking light will go.

STEP TWO: From the Viewer's Generator pop-up menu (the little icon with the "A" in it), select Shapes > Circle.


STEP THREE: Add the circle to your new layer of video. Trim the circle clip down to your desired length. The default should be a colored circle on black. Control-click on the new circle layer and set your Composite Mode to Screen. The Screen mode will get rid of blacks and leave you with a colored circle over your video.


STEP FOUR: Double click your circle clip to load it back into the Viewer. In the Controls tab, set your size, softness and color.


STEP FIVE: In the Motion tab set your center point to align your blinking light with the bulb (or whatever) in your video.

STEP SIX: Turn down the Opacity arrow and set yourself some keyframes for your light. Drag every other keyframe down to 0% opacity and leave the others at 100% opacity. It should look like a horizontal zig-zag.


STEP SEVEN: You should be finished. Enjoy your blinking light effect!