vertex offset speed

I've been trying to change the vertex offset speed rather than intensity. I'm working from the example shader you included of the orange vertex animation, but adjusting values only changes the shape. I've tried adding a time node multiplied by value into a sine, but the fact of the matter is I'm just not sure what i'm doing. Any tips?
My goal is to make a fast moving snaking animation for a vein without blowing up the size of it too strongly.
Thanks