The relay would only account for the headlights, not the tail-light
Can you measure the voltage at both sides of Fuse 8 for me?
Do that with the fuse still in place - connect your meter with black probe on battery negative then touch the positive to the metal tabs on the top of the fuse, on both sides.
That will not only validate the Fuse but also give a data point whether there is voltage at that node, which can help point to whether problem up or down stream from there.
Just another sanity check please - were these LED headlights plug n play into the std H4 connectors, or did you modify the wiring at all to accommodate them?
And what brand/model of lights were they? Do they have a halo ring or anything that was powered to the Running Light Circuit?
Here is the Headlight Power Circuit for the R3R