Sounds like you guys might benefit from the tracer app we have on this side of the ditch. All businesses can (must) download a (unique to that business or location) tracer app QR code from the Ministry of Health website. You scan that QR code using a Covid App which then records that you were at that location at a particular time. It's basically an electronic diary located on your phone. There is no need for a cellular connection to be able to scan. The scan records are removed 30 days after the scan.
If there's a suspected Covid case at a particular location that locations details are broadcast to all app users via the app. The app can identify if that location is one of those stored on the device. At that point the app alerts the user to a possible Covid contact. The user then contacts the health authorities for further action.
Users can opt into sharing their location details in real time to the health authorities to allow faster tracing but otherwise your locations are not shared unless it has been identified you have had a potential contact with Covid.
It's introduction was a shambles but now it seems to be working pretty well.