My 1st thought would be magnet wire; stuff small motors are made with, coils too. But that has a varnish coating as the insulator as Ken stated. The thing that you might be concerned with is 40Ga current carrying capability. Ya can't put much down that pipe. 0.090A or 90mA. If those signals are LED, then each could be 20mA if you are using the output of some port at it's rating...I.E Atmel ports are capable of sourcing/sinking 20mA. Ok for the individual LEDs, but overspec on power or ground depending on how you have them set up and all are on at the same time. If you can limit to 15mA you are good, although the brightness will be less. Worst case would be fire and Insurance companies know how to look for that where your coverage might be thrown out the window. Maybe this is splitting hairs but it IS something to watch for.
Another case to watch for are those super bright garage type lights from another country - no Underwriter's seal and not covered by most Insurance.