I had a look at my Slick Chick and it starts a game with either green "Slick", yellow "Chick" or red "Slick Chick" lit, it does not start with a consistently lit insert.
Looking at the schematic, it at first appears that green "Slick" should be lit at the start of a game, as that is the only motor switch shown closed (1E)
However, a complete cycle of the score motor is 120 degrees or a third of a revolution, so the motor can stop at any one of three positions at the end of a game and then, when a new game is started, once it has gone through it's reset sequence, the motor can, again, be in any one of three positions, thereby closing motor switch 1E or 4E, or 5E.
If you watch the motor pin "E", this is the tallest pin on the top of the motor, this activates the relevent motor switches. (There is a drawing of the motor cams and pins as well as the switch positions on the bottom left of the schematic)

Hope this helps.

You're welcome.