So looking at how you’ve set things up, you can nix splines for now. What you’ll do instead is:
Grab a Cylinder from the geometry tab on your main window and drag it in. They look like this:
NOT THIS>>>>>>>>>>>
These geometries can be modified to make your lines by using the Brush Editor.
You’ll want to modify the brush settings to size the width of the cylinder first, probably like .5 or something really low. Think “Pipes” instead of “lines”. 
You can check this documentation out on the brush editor to get the hang of it, and there are a TON of tutorials out there that use it, I’m just not sure of any specific ones.
Then you’ll just have them be dark or unseen normally and change to glowy when their connection is selected using emissive materials, which you’re rather familiar with now!