I didn't have the final variable resistors hooked up in this picture.  I used some little potentiometers that I already had on the protoboard.  I took a video of the eyeballs in the dark.  They look pretty cool.  (see below) 

It is worth mentioning that your could use the EKI kit without alteration if you only want to drive 2 LED's for eyeballs.  My intention with this circuit is to drive upwards of 10 UV LED's for a bigger strobe effect.

Video 1

Video 2