There is a shader setting called Specular, or sometimes Gloss (directX 12?)
Usually we use a specular map to control the shininess.
Here is a File I made for NeoTextureEdit:
Where the white spots are in the specular texture will make the area Glossy, the black or dark areas will make it Dull and not shiny.
If you do not have a specular map in your shader you usually only have a number setting to adjust the shininess of the entire shader.1 will make it look like it is covered in snot, or 0 will make it unshiny like a pile of dust.
To build a parallax shader, you will need to use a Heightmap, a Normal map, and a Specular map, along with your color, or diffuse map.
The parallax shader will cast shadows from the bumps so you get an ULTRA real look to it.
More on Specular settings here:
Are you going to share your shader with the community when you are done making it? Is it WebGL?