Gray is the flasher wire that goes to the stock turnsignal thumblever. Your low-profile switch doesn't have terminals for the stripe wires (front running lights on your front turnsignals). In the stock configuration, the running light switch operates in tandem with the turnsignal switch. In other words, they're a double pole switch. Except this double pole switch shuts off the running light (low-filament) for the turnsignal (high-filament) that is activated so that both low-filament and the high-filament are never ON at the same time in the same bulb via an inverse wiring scheme (refer to my previous graphic). Also, from my side of the computer screen, it appears that your low-profile switch also lacks a terminal for your high & low beam switch for the headlight. The stripe wires can be connected to the low filament wires at their respective turnsignal socket (soldered or crimped). You'll have to add on a high/low beam switch for your headlight.
2007 Honda Shadow 600