A suggestion that I would have to actuate the button, at least if you are using a servo, would be to use a cam linkage to depress the button on the screen. If you set it to move to an angle past the actuation point when a color change is detected, it will "tap" the screen.
It's like the side of a train, sort of, in how it works- I hope the picture I've attached helps.
The output shaft is at the top of the image, and the spring holds the output shaft against the cam, so that it follows any grooves/ depressions/ rises in the cam surface; for example, rotating this cam counter- clockwise would cause the shaft to actuate, and then pull back, beginning to actuate again as it nears the elongated end of the cam when it has gone a full revolution.