Okay, there's a lot going on here and some of what you've said needs detailed correcting.
The Fender Blackout Telecaster, which you've taken this pickup from, comes stock with a '59 wired in reverse phase and a 'normal' Pearly Gates Plus. (Which is
not a Pearly Gates Bridge.)
The PG+ was first designed to be installed with Fender Texas Special single coils, and as such the winding direction and polarity are opposite to other Seymour Duncan pickups. It is made and wired so when it's split with the Fender middle RWRP single coil the two will be hum-cancelling and in regular phase.
If you wire it up 'the Fender way' (which is
not the colour code you described; see below) but use another (non-Fender) Seymour Duncan pickup in the middle or neck position of a guitar then the combined pickup selections (i.e. bridge+neck or bridge+middle) will give an out-of-phase tone. You can correct this and get the standard combined tone by wiring one of the pickups in reverse phase or by flipping the magnet(s) in one of the pickups.
This is why the Blackout Tele has the '59 neck pickup wired in reverse. The PG+ is made to match Fender, which is the opposite phase of Seymour Duncan usually, so the '59 also had to be reversed in order to get both pickups back in-phase. Why they didn't just use a standard matched set of '59s, since the PG+ and '59 Bridge are very similar anyway, I don't know, but ultimately it is just a simple wiring swap.
In any case, whether you keep the pickups out-of-phase with each other or reverse one of them, the pickups on their own will sound normal. It's only the combined positions that are affected. I do suggest you give it a shot with the pickups out-of-phase, since it can be a useful sound and 'correcting' it later is easy enough if you don't like it. If you're not familiar with out-of-phase humbucker sounds, listen to some Peter Green (pre-1970 Fleetwood Mac). Jimmy Page, Brian May and Joe Perry also all use out-of-phase tones quite often.
All that said,
I think you might have read your Fender wiring incorrectly.
This is the diagram for the Blackout Telecaster. As you can see, for the PG+ black & red are
not tied off as you say. (In fact I'm not aware of any pickup manufacturer that uses black & red for series link, ever.) Green & black are tied off as the series link, only the white goes to ground, and red is used for the hot. This is 'undoing' the pickup being wound reverse to the neck (the coil starts are now creating the series link instead of the coil ends and the south is being used for the hot instead of the north). I'm not sure why they did this since I think it would only affect the sound if the pickups were split, which is a feature the Blackout Tele doesn't have anyway. The '59 is wired simply to reverse its phase, green to hot and black to ground.
So
compared to normal SD pickups, this guitar has a RP neck and RWRP bridge, so on their own they're in-phase and if they were split (which, again, this guitar doesn't have) the split coils would be hum-cancelling.
If you look at
the diagram for a Lone Star Strat you can see how the PG+ is wired up when paired with Fender's own RWRP single coil middle pickup. Since the pickup is made to match those pickups and there's no need to 'counter' regular SD pickup construction, it is wired in like any regular SD pickup: red & white for series link (in this case, on the 5-way to auto-split in position 2), black for hot, green goes to ground. No special wiring needed since the pickup is already in the correct direction and polarity to be hum-cancelling with the Fender RWRP pickup.
So to wire up the PG+ into a 2-humbucker guitar with a regular SD neck pickup, you can do one of three things:
1) If your guitar will have a coil split switch, copy the Blackout Tele's wiring exactly, reversing the direction of the PG+ and the polarity of the neck pickup, with the green & black wires of the PG+ and the white & red wires of the neck pickup going to your split switch. This gives you an in-phase middle sound with hum-cancelling split coils.
2) If your guitar will not have a coil split, reverse the polarity of
one of the pickups by swapping the black and green wires. Red & white still join together for series operation. This will give you the standard in-phase middle tone.
3) Install both pickups using the standard Seymour Duncan code of black to hot, red & white for series, and green to ground. This will give you the uncommon but sometimes preferred out-of-phase middle tone.
If using a non-SD neck pickup, simply refer to
this chart to see how different manufacturers' wire colours translate.
Lastly, do check your pickup will actually fit in the LP before you embark on wiring the whole thing up. Most PG+ pickups are made as trembuckers (I say "most"; all the ones I've ever owned or seen have been trembuckers, but I've heard unsubstantiated claims that some early ones were made as regular humbuckers) and don't quite fit into standard humbucker mounting rings, and the poles won't align with the string spacing of a standard LP tune-o-matic bridge. If the PG+ won't fit then you can use a '59 Bridge to get 99% the same sound instead, or a regular Pearly Gates Bridge and swap the A2 magnet for an A5. (Which will sound
a little bit thinner than the PG+ but still in the same ballpark.)
edit: Now I've written all that (which I'll still keep since people often search these boards for info) I see now from Jack's link you're trying to pair this with a (regular?) SD '59 neck. In that case, and assuming you want totally standard tones from both pickups and the middle position, simply follow the wiring diagram for the Fender Blackout Telecaster that I linked above.
