It is undoubtedly a Hidden textstroboscopic gun for timing something. If you hadn't said alligator clips I'd be on firmer ground in saying it's for timing car engines, but the chances are this originally came with other bits and pieces to make it do its job. The side view had me ready to call "Taser", but the lens is a giveaway. I think.
[Dujon, Stevie] Exactly so. One cable has two clips that go to the battery, the other has one clip that goes somewhere to pick up the high voltage spark and trigger the xenon flash tube. I'm thinking of pulling the innards out and replacing them with some sort of sound and light generator.
[Raak] So, you misled everyone by lying (by omission) about the cables! Now I'm in two minds whether to tell you that the third lead goes into the cap for sparkplug number 1. In fact, I think I won't. Nor will I mention the long metal electrode you need to attach to the sparkplug so you can connect the dizzy and the raygun of soon to be chewed-up-in-the-fan fingers.