IIS: logging client certificate's thumbprint
Solution 1:
While I am not proficient in IIS in particular (I deal with Apache mostly), I would expect this is be a custom logging sort of thing.
The following page documents some of the advanced logging functionality of IIS; while it doesn't show SSL things in the screenshots, it may still be useful.
http://www.iis.net/learn/extensions/advanced-logging-module/advanced-logging-for-iis-custom-logging
Note also the doucmentation around IIS server variables, which I would expect to be able to be logged in a custom logging situation.
https://msdn.microsoft.com/library/ms524602.aspx
That page does list various Client Authentication server variables.
Cheers, Cameron