Nee help with multiple light streaks converging

I’ve made a crude animation of what I’m trying to accomplish that you can see here.

I’ve been able to accomplish the light streak using several different methods (ex. particles and halos) but I can’t seem to get it all to come together. Namely, when I link the particle to follow a path it no longer looks like a streak but a series of glowing dots. I also can’t figure out how to control the speed of the particle as it travels along the path.

Any help would be appreciated. Thanks!