Disconnect the Green and White from the push/pull (in case it is shorting/broken internally), and connect the Green to the Red on the pot lug. That should tell you if the Green/Black coil is working (assuming the Black is still connected to ground).

A Multimeter is still the best test option. Disconnect the pickup and check the resistance across the coil pairs, that will show what’s working and that all the colours are correct. Just in case. Test the push/pul too.