Do you mean to illuminate the handle-well so you can see it at night? I don't see why you couldn't wire some small LEDs in to the mechanism tbh. Optical fibre might not handle the movement of the handle too well, but a couple of tiny surface-mount LEDs wouldn't be too intrusive.
You could trigger it from the interior light I think - that comes on when you unlock the car doesn't it?
Might be a nice touch
