JimmyP1000 , this is specific to the appliance you would be using. Best to ask the vendor if logging can be enabled and how the logs can be retrieved.
On the Exchange Server side, you would be checking these logs to see if the request from Exchange Online reached Exchange / IIS server:
- IIS logs / HTTPProxy logs / HTTPerr logs when reproducing the Free/Busy issue from EXO User to On-Premises user(s).
- Network trace (like Netmon) when reproducing the Free/Busy issue from EXO User to On-Premises user(s).
You can use Free/Busy Test on Remote Connectivity Analyzer: https://testconnectivity.microsoft.com/tests/FreeBusy/input , this way you see the Free/Busy error, if DNS part is fine, ports unblocked, certificate and SSL/TLS connections ok. The Free/Busy connection will be coming from an Exchange Online IP Address (if cloud side is configured ok) but Autodiscover call will be coming from an the tool IP addresses Remote Connectivity Analyzer Change List (microsoft.com)