Remember, fiber optics do not shed enough light sideways. They do a great job directing light along their length, but that comes at the price to where little is wasted outside the cable. I want to check out the Alembic that was mentioned with LED markers that supplied line light power. Like many Alembics, I'm sure it had phantom power, and with the supposed number of LEDs and whatever electronics, it'd come as no surprise.
A trick I learned from Martin Keith when doing some work for Veillette:
correctly drill a hole the diameter of your optic cable through a piece of clear acrylic that has more depth than an LED light. Drill, using the established hole, another hole that will hold the LED. When you've inserted both elements into the acrylic, wick in some super thin CA glue. Of note, file and sand clean (flat, too) the optic cable for maximum transference. If this application could be run in and out, and even split (as I would think Alembic did), then we should be able to do it too. The main issue, IMO, is power. Easy enough: powering LEDs, running that light up optics, scattering along a thin acrylic sheet for the fretline. Not so easy (yet): evenly powering multiple fretlines with one LED, powering that many LEDs with onboard power, and fingerboard wear issues.
Who's got a link to that Alembic?