When I did this, admittedly a while back, I did something like pass 4 coordinate pairs in per line -- two at each end. I then used the vertex shader to spread them "out" from the line along a vector which is at right angles to the line and the eye vector (passed in as a uniform). That makes a billboard covering the line's projected position. The vertices have texture coords set up to run (0,0) -> (1,1) across the space with one axis running up/down the line and the other "across" it. The pixel shader can then use the proximity to (0.5,whatever) to put the glow in.

It's performant enough to run on mobile devices without too much aggro.

It's not *quite* technically right, because you're supposed to use the vector between the point and the eye (rather than just the direction the eye is pointing) which changes across the FoV, but if the FoV is relatively narrow, no-one notices. It's also a bit unstable if the lines are close to the camera, but... don't do that?

For picking the lines, I cheated some more and used a transform feedback array -- the lines fill in their depth if they think their projected points are close enough to the point clicked and the CPU then just scans the array looking for the nearest close result (Grabbing a transform feedback is expensive, but if you're only doing it on clicks it's not too bad.)

You could pass in the XY of the last click and have the vertex shader check the position to see if it's close before deciding whether to add glow & expand out the endpoints.