I think the simple answer here is "not possible".. You live you learn, see answer on ASP.NET Performance counters. I'm very interested on how that goes (if it works for you), and if it gives you application specific data (vs. aggregate of all applications on the box?).
Even the suggestion to look at log files will not get you what you want - as you're looking at the log file, how would you know there isn't a user starting a session?
Sessions are cookies to a browser. So if visit 1 page in your web site, I leave your website and go to some other web site, and then come back (before whatever timeout value you set)? How would you define that? At the point I left your web site, you will not see "any" activity (whatever monitor you use), but that doesn't mean my session is "expired".
It doesn't even have to be that complicated - I visit your web site, and start reading your content (not navigating, not doing anything that can be measure/monitored).
I guess there's more clarity needed on the "goal" - as in what are you after? The objective of resetting isn't the real "goal" of what you want to achieve.
Update:
I know you said you can't modify the source code, so you can hope that it implements Google Analytics. If so, you can look at the real time activity of your web site. This at least gets you "somewhere" in some trivial fashion. BUT just the same, the "magic" is based on cookies (which therefore means its still subject to the questions I posed above)