For full Salesforce synchronization, the account owner should be a Salesforce Administrator. We would prefer to use less permissions if possible, but this is a limitation of Salesforce at present (the community have been waiting 8 years).
Specifically, the Modify All Data permission is needed.
Why does Jiminny need this?
Simply put, we sync various data between Salesforce for the purpose of providing the service. This includes:
Matching email addresses and phone numbers to your customers
This allows us to automatically populate meeting details
Retrieving standard and custom field data
This is used to enhance activity logging, as well as importing picklist values
Retrieving customer and opportunity/deal data
We add this to playback and any shared activity to give it context