Is there a way to find on which server the BigFix console is installed on, simply by looking through logs on the ILMT/BigFix server (or some other means) ? Or can we just re-install the console on a new Windows server ?

In case it helps someone else, the IP address of the BigFix console can be found in the server audit logs which are:

%ProgramFiles(x86)%\BigFix Enterprise\BES Server\server_audit.log or

/var/opt/BESServer/server_audit.log

on the Root server.

Search for the word "CONSOLE" and it will display the IP address of the console.