I would seriously evaluate low voltage lighting for this task, as it will let you use cables with more liberalized rules.
However, in your case I would run PVC (yeah, take a picture, me recommending PVC!) conduit, with a conduit body exiting the bottom of the receptacle box, running just below the bottom of the sheathing... then another conduit body to turn the corner horizontally... then another conduit body to go straight up on the left side of that cap... then yet another to hug that shadowy eave, then tee's out to wherever your light positions are.
Remember to run ground in the PVC, or do the whole works low-voltage. When you use Class I wiring methods like the above, it removes the 55W limit on low-voltage (it's a bit more complicated than that, but...)
Lastly (or firstly because then you can rattle-can it), scuff-sand the PVC with a 3M Scotchbrite sponge/pad (green), then apply primer pref. alkyd (e.g. Kilz Original or Rustoleum 7780), then topcoat to match the house. That will greatly improve the camouflage, and more importantly, will protect the PVC from solar UV damage, which will tear it up in a couple of years if you don't.