I'm after a cheap light head with a 1 second or so strobe length.

So far everything I've purchased or read about has a strobe so fast its sole purpose is to cause epileptic fits in both rider and observer.

One of my many lights is the SolarStorm X2. It's better than most but still too fast (and also too bright in strobe mode).

This is for road use with a custom lens to prevent blinding oncoming traffic.