Gradient Around Specific Edge (Eevee)

What the title says. I’m trying to figure out the best way to put a purple gradient around this edge of the eye. I’m pretty sure texture painting is the best way to go, but I’m not experienced with it whatsoever and don’t know where to start.

What I’m going for:
image

Difficult to say without seeing the geometry. What is it for? Do you want to export it or does everything happen inside blender. Still or animation?
maybe you can mask the region with a vertex group or create vertex colours and drive the material with that

It’s subdivided with a temporary bevel mod currently. I have no intentions to use this rig for anything aside from still renders in blender.
image
I’m not too familiar with vertex groups either, could you enlighten me on that process you mentioned?

There are several posibilities dpendening on your knowledge, workflow and other things about the model…

If using a texture map then exporting the UVlayout and using it to mask an area in some painting app and “simply” paint that gradient… or using vertex colors to make that gradient… maybe even using both and do some mixing of this maybe even using some a baked texture version of the vertex colors…