Thanks all, for the ideas.
The vibration thing is out because then your focus is on the back of your neck, or wherever that thing is pressed up against. Plus, would you want someone pressing on the back of your neck as you're trying to relax and get into the zone before a run?
I am leery of having the SO drag around a cable. I want the light in front of me somehow, and if it's a stage where I have to move, I don't want to have to worry about tripping over a cable.
I am also a photographer, so I have a lot of photo equipment. I am going to get one of these timers (still trying to figure out which one), and connect it to a radio remote trigger. These radio triggers have a jack input, so I just need the cable that goes from the timer to the remote. The remote will trigger another remote, which is connected to a speedlight. Need to make sure that the timer can talk to the remote without frying it. I have electronics-savvy friends. So far, they are optimistic. This is a very expensive solution, however. The triggers are 185 bucks each, and the speedlight is another $100. (I may invest in a cheap set of triggers just for shooting, so if they get shot or broken, it's not as painful.)
The SO would have to carry the timer and the remote, connected via cable. It wouldn't be that big, but it's not as nimble as the timer alone. I'm thinking maybe rubberband them together so it's not floppy.
I'll see how it works. If anybody else has any ideas, I'd love to hear them.