http://www.shadedrelief.com/ is a good resource for many such techniques for converting a heightfield such as a DEM or hand-drawn element into pretty shaded relief. Most of the techniques are not using The GIMP, though.

The GIMP's Bump Map filter (https://docs.gimp.org/2.10/en/gimp-filter-bump-map.html) should give good results. You should be able to put the bump map on its own layer and then blend that layer on top of your color layer using transparency. Using a straight multiply blend can only darken the colors, not lighten them.