Looks like the main PCB sends out (low level) signals to the triac board, which in turn controls the (high) power to the lights.
Should work fine controlling most anything 120VAC... What'd you have in mind?
Be aware that some things might not work well being on very briefly (like CFL bulbs), and you may have issues with "inductive loads" (e.g. motors) not turning off properly. Looks like the triacs are rated for 2.5A... I'd try to keep it comfortably below that.
Oh, I thought you were wanting it to drive something other than incandescent light bulbs.
No, there are no "brains" on the triac board. It's essentially just a dual AC relay. As kstillin mentioned, you'd need something else to generate the alternating on/off signals. Google for "alternating LED flasher" or "blinker" and you'll find a variety of circuit designs to do this. Some use a 555 timer, others use a pair of transistors... and of course, as kstillin also said, an Arduino (or similar microcontroller board) would also work (and also cost like $30, and also be major overkill, unless you wanted to program various blinking patterns/speeds/etc.).
Don't forget, the triac board needs +5VDC power, and whatever you make to do the blinking signals will also need power, so you'll have a power supply (e.g. wall wart) in there too.
You know what this made me think of?
The stupid Christmas tree flashers with the 8 different patterns!
We put up the tree last night and I sat and stared at the three sets of lights for like 20 minutes. One of the sets was stuck on the same pattern and every now and then, the other two sets would hit the same one. Pretty neat.
I think the little controller drives three different banks of lights- red, yellow, and blue. There may be some asymmetrical patterns if you try to control the pair of APB lights like that, but it would be a cheap hack for what you want to do.