Using and animating characters with morph targets without glitches?

Why? See this is an instant benefit of always making your own stuff. it becomes super trivial to fix it.
Open the character in Blender, set up a “paint” material, assign the whole character to it, look up the UVs to make sure the correct one is being used. Paint the whole thing black. paint the area you want brighter white.
Save the texture out.
Bring the texture to unreal. the model and blender doesn’t matter at all.

Add a texture sampler with this texture to the skin material, use it as an Alpha to brighten the spot you need without touching the rest.

Obviously this doesn’t “solve” the light issues, but if all you want to do is lighten or even put emissive in just that area, this is it.