The pickups are single coils. I’m guessing here, because I’m not familiar with Teiscos, but I reckon you’re right about the black being grounds (practically universal) and the red and whites being soldered in an alternating pattern. This, I think would have the neck pup in reverse polarity to the bridge pup. Hence, the single-coil hum would be cancelled rather than reinforced when both pups are selected.

That’s my guesswork, but I know our contributor (SB) runs vintaxe.com and, apart from having catalog info, one like yours was sold via his site. He may be able to put you in touch with the owner. If he doesn’t look in here swiftly, perhaps you could try a PM.