Hi,
This may not be the optimal way, but how I do it:
Model the cove recess detail nicely (the part where the led is concealed) so that the light will bounce evenly.
Draw the path of the LED strip as a spline + sweep modifier (bar section) + edit poly (ring select edges to delete all faces bar the 1 side that will be the LED strip)
Apply Corona Light Mtl.
This way you can adjust the sweep width (i.e. led strip) offset and angle easily, in combination with Light material directionality and intensity. It's usually a balance of all of these.