Bill,
Can you check my "work"?
The right side of the relay is the coil side (the left is power in and out to lamps; thus, the right side controls the off/on).
Cuts must be made in two general locations: (1) coil out (black/ground) to junction (junction of grounds for both lights, coil out, and wire to battery negative); and (2) switch power in to coil in/ground to coil out (which, combined with (1), eventually leads to battery negative).
With respect to cut (1), tap the wire out of the coil out and run it to the stock switch "in" [pin 3] (essentially ground in). Then, tap stock switch "out" [pin 4] and run wire to other half of cut (1). Thus, coil out exits the relay, runs to the stock switch, comes back, and is tied to the junction.
With respect to cut (2), tap parking light source and connect white. This provides the positive power for the relay so that when the circuit is closed (the stock fog light switch is turned on), the circuit is complete and the relay coil allows the power to flow to the lights. The ground that comes from stock PIAA switch is not needed and is capped and taped.
Sound right?