We wanted to document this one as had not seen it before.
The S4S Mapping wizard was working fine, indicating the credentials and access were all in place. We also checked that there were campaigns set to Active, as inactive campaigns will not be retrieved from SF.
However, the Campaign list would still not populate.
As it turns out, there is a setting on the profile of the user credentials used for the connection (API user). The Marketing User checkbox must be checked to access the Campaigns.
Here is a screenshot from one of our test sandboxes to illustrate this checkbox setting.