If Dooku is a Sith why didn't he get them, if it's a hulk thing and they only come on when the power is on why didn't Anakin have them in AOTC, why doesn't have then all through his Vader moments, why doesn't Luke get them in ROTJ?
As far as I understand, the Sith eyes appeared for Darth Maul as means to make him cool and menacing (I wouldn't call Palpatine's eyes in RotJ Sith eyes... they're relatively normal). Then, in 2003-2004 (AFTER AotC, mind you) KotOR games have been released, where those who follow the Dark Side slowly change appearance (most notably the eyes). The idea was then applied for the 2005 RotS in a way.
This is just another example of Lucas thinking about something on the way, as he was doing ever since the first sequel to Star Wars was in the making.