Does "zero reading" mean you measured a resistance of zero? Really zero, measured on a low-resistance setting of your meter? Examine the external wiring very closely with a magnifier, looking for anywhere it could be shorted.
I doubt that the pickup suddenly developed an internal short while the instrument sat in the case. I'd tend to suspect there was another problem like corrosion on the pickup selector switch (which would not be surprising if it wasn't used for a while), and the short you're now measuring happened when you unsoldered it to remove it.
Umm, you didn't try adjusting the pole pieces, did you? They look like they should be adjustable but they are not meant to be turned. They hold the pickup together, and the coil is wound over a little bit of electrical tape around the screws. Turn the screws and you wear through the tape and short (or break) the very fine coil wire. I learned this the hard way, several decades ago.