I am trying to run a string of four lights outside of my place of business to brighten the parking lot at night.

I am using 12-2 UF-B with Ground Outdoor Electrical Wire, a 40 amp timer, and four lights (rated at 120 v and 60 watts each).

I have everything ran, but when I flip the breaker on, the light bulbs blow out, starting with the last light, working its way back to the first light from the breaker. And this process takes about 10 seconds.

I've gone back through to see if any wires were touching, but I don't see anything out of the ordinary. I've also hooked up each light to a power cord and plugged them into a receptacle to see if they were bad. All of them worked fine.

I'm sure its something simple that I'm overlooking, but for the life of me, I can't figure it out. Any help would be GREATLY appreciated!

Sounds like maybe it is seeing high voltage (240)? Or low voltage bulbs.
Make sure bulbs and supply are 120 volts, breaker needs to be 20 Amps, Single pole.
You could use a 240 volt timer, but wire so it sees 120 volts. Neutral will not make a connection to timer terminals.

Sounds like you're hooked to 240 to me.

So, what voltage are you connecting to?