I would avoid any contact with the fiber, that could leave residue on the end, dulling the glow. Yoursafestbetis to RAISE the pin you are working on, and SINK ALL of the others as as they can go.

But honestly, just remove the fiber, melt the end with a paper match - slowly raising the flame until you get that bulge ()...the immediatly remove the flame.

Replace the fiber into the pin and route it down through the protective sheathing...

I see it is a Rhino sight - is it the version with the Fiber Cage? If so, that changes things a bit!