What factors affect the brightness of electroluminescent wire?
Caveat: I've not built EL wire, but having read some articles and having the background to analyse this here are some guide lines.

How it works:
An electric field kicks electrons up to higher orbitals within the phosphor molecule which when then decay/emit light. This orbital decay and light emission will be very fast (called prompt emission)but we'd need to know the phosphor characteristics to be precise.  But certainly ns to us range is reasonable.  That means that for every AC cycle you get a pulse of light, if you have higher numbers of cycles in a second you get more pulses of light and therefore it is brighter.

The higher voltage effect is a little harder to understand.  Strictly speaking, once you've ionized the phosphor the additional voltage will go into heat for a given electron in it's orbital.  But depending upon the particular phosphor, if it has higher vacancies available then the electron might skip to a higher energy and then emit a subsequently higher energy photon (bluer in color).  This is again dependant upon formulation of the phosphor.  So if you look at an individual molecule you can't explain why higher voltage gives you higher light output.  I strongly suspect that it has to do with the fact that the electric field around the thin wire excites more of a volume of phosphor at higher voltages.  As the voltage increases, the e-field lines move further out, which then interacts with more phosphor which means that there is greater light.

With this in mind how do you increase output?


Make your windings closer together, you have a trade off with the wire blocking more light and the E-fields being more strongly overlapping and exciting more volume of phosphor.  Commercial EL wires use a transparent electrode that wraps around the phosphor eliminating this effect (i.e. uniform E-field).
Jeri coats the wire on the outside with phosphor, the E-Field is lower outside of the wire, so if you can coat the whole assembly with transparent HIGH dielectric insulating material, more of the E-Field will exist on the outside where the phosphor is.
Get a core wire with an insulator that has LOWER dielectric constant, this will cause the E-Field on the outside to increase.  If the  dielectric constant of the core wire is already low then there isn't too much you can do.
Try different configurations: remember that E-Filed is Voltage divided by distance so a lower voltage as a tighter spacing will have a high E-field.  I can think of several variations.  Two thinner wires wound around each other, 4 very thin wires would around each other with alternate pairs connected together.
Safety note:  if you are building the coaxial design (as per the video) drive the inner electrode with the HV, it will be shielded just that much more.