Should I replace the token within my Square Account and look for a reset message within the module?
If the Locations dropdown is not empty when you click Edit on the module, then usually that means the token is fine.
You can also just visit https://your_site.com/square_handler.php in your browser and it will auto-refresh the token if possible. If it fails then in the module Admin page the green "login and authorize" button will appear and the module's status will be set to false.