Here's a hint: if the neck pup always plays, the neck pup's negative lead has a path to ground, and is NOT going through the switch exclusively.
You seem to be confused about how the switch works. There's only ONE throw where the left and right sides are connected - throw #4, the series combo. Here's a quick drawing that I did, perhaps this will help:
The lugs with the "C" next to them (at the opposite ends of the poles (rows of lugs)) are the COMMON lugs for this switch - they are the constant against which the other lugs are switched. You can readily see how this scheme switches the bridge's HOT lead and the neck's NEGATIVE lead, with the neck's HOT lead always connected to the volume pot.
If you look at the two lugs with the "1" near them,
you will be able to trace the signal path like this:
The bridge pup hot (and neck pup hot) connect to the volume pot.
But, only the bridge pup plays, because the neck pup's negative lead is NOT grounded.
For "2", the bridge pup plays AND the neck pup plays, because the neck pup's negative lead now has a path to ground.
For "3", the neck pup only plays - the bridge pup's hot is NOT connected, and the neck pup's negative still has a path to ground.
For "4", you get series - the neck pup's negative lead is now connected to the bridge pup's HOT lead, so they play in series.
Not shown in this drawing is the neck pup's ground/shield lead - it has NOTHING to do with the switching, and just gets soldered to ground.
As you look at the drawing, notice that the two poles (rows of lugs down the side) are reverse-symmetrical - in other words, turning the switch 180 degrees and rewiring (as Drak tried) has no effect on the function of the switch!
One other thing that COULD be an issue here - I've seen this on Strat 5-ways - is that you may have a non-Fender switch with a different lug layout. I haven't seen a 4-way like this, but there's always a first time - so it would be odd, but possible...
In other words, the common lugs may be at the other end of the poles - instead of bottom-left and top-right, as shown in the drawing, the switch may have been manufactured with top-left and bottom-right as commons.
This is a common issue when people use the replacement 5-ways from Stewmac.com and a few others in a Fender axe - the commons are at the "wrong end" of the row of lugs (poles). And I don't EVEN want to get into the Mega-S switches!
If this were the case, then all you need to do is "mirror-image" the drawing - reverse it left for right - so that the commons in the drawing match your switch. You should be able to meter-check this, or heck, even just eyeball it by looking at the wiper.
Does that help?