Find out what MAC address he uses(using something like wireshark) spoof your MAC address while he is connected and it’s a less then well thought out proxy server that might be enough.(Mind you this obviously won’t help your customers)
If that doesn’t work just keep monitoring the packets and if it’s http rather than https you should be able to follow the tcp stream of him entering his credentials. Then share it with everyone who it’s meant to be used for(best to write it lying around on a piece of paper rather than actually telling people) . When he realises that it’s being used by others rinse and repeat until he either learn his lesson or gets smarter. If it really is meant to be shared complain to his one up.
Sounds like a RADIUS server your best bet would be to sniff all traffic with a device when you’re not there. Find the MAC address and IP (IP is subject to change) of his device and isolate what traffic you are sniffing. He is bound to re-enter his credentials again. Happy hunting.
What is the purpose of a store wifi that nobody is allowed to use? Appeal to the social side of the matter. If your manager is not high up enough to force the GM to let you use it and you can demonstrate a legitimate need for access, ask your manager for help either going over the general manager’s head or set up your own wifi.
Perhaps the GM is not confident in the security of what he has set up yet, and you can gain his trust by pointing him to resources that help him secure it better. Become his IT go-to guy so you get to be in charge of the thing. This is the part where I remind you that hacking an employers network can get you not only fired but jailed.