Auditing use of gnomesu

Hi folks. I’m in the process of writing a short bash script that uses zenity and gnomesu to have users of a shared machine start Firefox as their own user while the machine is logged in as a generic user. The one piece I’m missing is a fairly important one to the requesters of this change: I need to be able to find out which user was using Firefox at a particular time on the machine.

Sudo logs to /var/log/messages when someone runs a command through it; that’s the sort of thing I’m looking for. Can gnomesu do such a thing? (I could of course just have the script make a simple log of its own, but then it would be set with permissions that allow the users to manipulate it, which we don’t want.)