Apply noise (or other procedural texture) to part of object?

Hi folks,

I’m hoping someone can point me in the right direction with this.

Please see the vid below (Blend file also attached).

In it i have a band of color moving from one side to the other on a plane.

What i’d like to do is to apply some noise (or wave texture) to only the right hand part where red meets black. I mean it should transition into black in some distorted noise or wavey manner…and on the left part of the red band (where it transitions sharply to black), that part should be unchanged.
And this distorted part should also move along with the band as i tweak the vector math node.

I feel sure it must be possible, i just can’t hack together the correct combination of nodes.

Thanks, hopefully in advance!

shader question.blend (683.6 KB)