I'm trying to replicate what this user was after, but without using particles. (I know the particles will work easier, it's just not what I want for this.) Glowing Light Trail in Eevee
I've got an emission shader on my curve object, and a path for it to follow. It's animated along the path, and what I want to do is fade out the tail end (the Bevel Start) as the curve animates, to create a simple light trail using geometry.
I was trying to do this with mixing a transparency shader and an emission shader with a color ramp between them, but that only gives me a smooth transition across the entire object, instead of fading it along the path.
Here's the scene I'm working with: light trail testing geometry
and a couple screencaps of what I have, what I'm after (just an image edit) and my current shaders

