In the service logs for for both Web Player services and Automation Services neither the ClientID nor ClientSecret is logged when accessing data, so it will not be possible to know which ClientID was used by just reading the log files.

How to verify which ClientID/ClientSecret is used when accessing data with Google Big Query/Analytics connector

Examine Spotfire.Dxp.Worker.Host.Debug.<ID>.log file for the desired service:

When ClientID/ClientSecret is obtained from the preferences there are two ways they could have been obtained, either from the Adapter specific preferences (i.e. Google Analytics or Google BigQuery) or they could have been obtained from the "Google Authentication" preferences, common to both Google Analytics and BigQuery.

If the adapter preferences are used the following line should be present in the log file:
Creating authentication settings from adapter preferences.

If the Google Authentication preferences are used you should see the following:
The ClientId and/or ClientSecret preferences are either missing or invalid for the current adapter. Falling back on Google Authentication preferences.
and
Creating authentication settings from Google Authentication preferences

In the Administration Manager you can see these preferences, i.e.  Google Authentication (used if the Google Analytics or BigQuery preferences are missing) and the adapter specific preferences for  Google BigQuery and  Google Analytics respectively. See screenshot for reference: 



In the same log lines you can see for which user these settings are read.