The wifi extension and its dependencies are not included in the piCore image.
I burnt a new piCore-13.0.3 sd card for an RPi0W about ten days ago, added wifi and everything worked first try
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Basically:
* burn the image to sd card
* extend the second partition (I also added a third swap partition)
* copy the firmware-rpi-wifi and wifi extensions (*tcz, *tcz.dep, *tcz.md5.txt) and their dependencies to /mnt/mmcblk0p2/tce/optional
* add firmware-rpi-wifi and wifi to /mnt/mmcblk0p2/tce/onboot.lst
* add "wifi.sh -a" to /opt/bootlocal.sh
* create ~/wifi.db for your access point
* make a backup
* reboot