Re: HS Duo Sonic with Invader question
The switch on the push pull know should have 3 pairs of terminals and be wired using middle and outer (one or the other outer). To switch the behavior, as long as everything is wired okay otherwise, just move whatever wire or wires is/are on the current outer terminal to the other outer terminal.
Edit to add: I happen to have on my shelf a push pull from a Fender Ensenada guitar as would be the same in your guitar. Checking with the multimeter suggests that wiring should use the middle position terminal and the terminal closest to the pot itself to achieve pull split aka grounding the second coil when pulled. Looking at the soldering leftovers I seem to recall that it was wired stock with the terminal closest to the pot as the ground by shunting from here to the pot, and the appropriate wires from the pickups were thus installed on the middle terminal.