Ok - There are these large black felt-tipped pens with alcohol solvent.. They are really dark, and the ink dries permanent.. I am not a chemist ;-) but suspect the pigment isnt carbon based... There is also the Sharpie markers, and I would be surprised if their pigment was carbon..
Is there some reagent with which one can test for carbon? I remember as a kid playing with dangerous chemicals (Benzine, mercury, bromine, carbon-tet, trichloretylene - to name a few) and seem to remember bromine doing strange things to my pencils graphite... (I was also fascinated by passing currents through different mixtures, watching an egg white go green for example - I now suspect it was more due to the copper wire though..;-)
If you can get a simple chemical, and test a Sharpie, that might be the easiest....
If you do find a suitable blackness, (and survive the experiment) please let us know!
ps - phosphorescence is really interesting, and I am surprised this type of paint is used, because I understood that it was based on metal compounds - but I am not sure - and particularly not sure if these are salts which perhaps do not have much conductivity - its one of the billion things I am curious about, but not curious enough to place investigation far enough up my list that I will look into it in this lifetime ;-)
Oh, just a completely OT aside..
I had an accident with a bottle of cynoacrilate adhesive (super glue) a couple of days ago - spilt a big blob onto my desk - I grabbed some kitchen towel to mop it up, but a few seconds after the paper touched the glue it burst into flames! Fortunately I have a piece of plywood on my desk when I do dirty jobs, so was able to lift the whole lot and take it outside and douse it in water...
Ever heard of anything like that before? - I wonder if it was some additive to the paper towel..