Make a separate comp with each line on a separate layer and make that comp as long as your final animation (all lines in the one comp) Then apply an effect on each layer to turn the color of the line to white – there’s a bunch – you can try tint or any of the change colors etc – you can do one layer and then copy and paste the effect to them all. If you’ve kept them as splines you can just change the stroke color in the layer settings or use as stroke effect.
Set each layer to “difference” for its transfer/blend function (again select all and then just change one and they will all change). There should be no background layer in this comp.
This should net you a lot of little black dots where the lines cross (assuming your comp color is not set to black).
Now precomp all of that and call the precomped comp “Lines” , then apply an invert effect to the precomped “Lines” comp and slip a black solid underneath. Now you have a bunch of white dots on black. Lets call this comp “Dots”.
Now in the Lines comp, vary which of the lines are transparent – you could do a random expression on the opacity attribute on each layer to automate this and clamp it to 0 or 100 or you could key frame each one with hold keyframes, or you could key frame one of the lines and then copy those key frames to other lines and offset the keyframes so it’s more random – if you now look in the Dots comp you will get a a bunch of sparkling white dots over black as the animation runs.
Take the Dots comp and screen it over your master comp and the white dots will appear wherever the lines cross and they will sparkle on and off.