Not sure I understand the question. . . so correct me if my answer is not what you were looking for.
The Grafik Eye should be connected in a junction box, like a regular 120V light switch. Black to Black, White to White, GND to GND. The rope lighting would be hardwired to the Grafik Eye in a similar fashion, Black to Zone X output, Neutral to Neutral.
Dimming a standard convenience outlet is against NEC code and should not be done. . .although I see people do it all the time. If you were to put a receptacle on a dimming circuit, Lutron makes a special receptacle and mating plug exactly for this purpose.
Craig