Could you please tell us which data source are you using? Based on my understand, you are using PowerBI Gateway connecting to a data source in cluster, one server with TLS enabled while another one not.
Have you checked if you can use other client to connect to this cluster of data source? Based on my experience, if it is SQL Server in a cluster, we may meet problem when one server with TLS while another not, I would suggest you checking the data source end error log. Generally, they will provide related error message.
Thanks for the reply, yes the majority of them are SQL Server data sources , one of them is an ODBC connection to a Denodo server.
Which logs do I need to check - the on-premises gateway log ? ... do I need to enable additional logging on the gateway and what is the specific kind of event I'm looking for in the logs (if you know, will save trawling through it ...)