If you want to switch the phase of one of the 2 coils shown in the picture, put the phase switch across the coil of the one you want to flip before the selector switch. Usually, however, phasing 2 coils of the same pickup won't result in a usable sound.
You already have "hot" and "not" outputs from the switch, the lower 2 lugs. These can be used for switching "down the line", so to speak, including phasing of this whole pickup.
The lower right-hand lug, as shown on your diagram, does not need to be grounded right there at the switch, it just has to find a ground somewhere along the line. Likewise the shield wire; these are depicted diagramatically as going to ground, but it is understood that that connection may be made elsewhere. In the case of the shield wire, you would want to ground that as far down the chain as you can, to avoid possibly introducing noise into the signal path.
I don't know for sure if it was clear from newey's post, but if you're going to do a phase flip, you don't want to be flipping the shield to the hot output, so you will not want it to connect to the "South Start' before reaching this S/P switch.
I guess maybe, it was fairly clear, but I've reiterated...