What is this "light trail" effect called - and how can I reproduce it today?
I don't know if it has an official name but could be classed as "ringing". Tube cameras would do it if you had any bright lights in the scene. 70's music videos are full of it.

You don't mention any software, so I'll give a platform agnostic solution. This would probably be easier in a node based workflow, but I've included the AE names for things because it's what I know best.

You could use a threshold effect ("extract" would probably work in After Effects) to grab just the bright parts of the image, and feed that into a delay ("echo" in After effects) then adjust the colour before compositing it back on to the original layer, probably using an additive compositing mode ("add" or "screen" maybe in AE).