What grade of fibre is used in optical fibre displays?
I think I have found what I am looking for.

PMMA Optical Fibre End Glow seems to be the standard term. PMMA being the plastic material of the Plastic Optical Fibre (POF).  "End Glow" refers to the end being the light output, as opposed to side glow which is also used in optical fibre lighting.

It is available in multiple widths (0.5mm, 0.75mm, 1.0mm, 1.5mm, ... , even up to 6mm), sheathed, unsheathed and sheathed with multiple strands. 

Looks like it can be bought from Alibaba or eBay (it looks like fishing line) or from lighting installers such as this one.