I think Driver's effect was geometry based. It would have been prohibitively expensive to do with shaders back at the time. Did we even have shaders back at the time?
Deadeye's effect is beautiful, you could also spawn trail segment sprites in the correct positions/sizes in a special layer and then blend that layer additively.
If the effect is to be done in screen space (trails stick to the screen) you can get screen-space position by doing posx-scrollx, posy-scrolly
If anyone can improve on this it'd be great (like, get rid of the seams!)