Advanced Line Masking?

So I’m making a webpage intro that has three curved lines, all coming in one by one. The client also wants a “highlight” or “pulse” to run across the lines. I made a copy of the lines and created a mask so that a small white pulse would appear to go across each curved line. The problem is is that it looks like poo. The edges of the ‘pulse’ are sharp, and I cannot get them to actually look like a reflection of light. Is there any way of doing this with a gradient or something so that it actually looks like a light reflection? Thanks