Hi Matthew,
Welcome to the forums!
As far as I know squid doesn't track this sort of info, and has no easy way of doing so. The nature of the internet makes this hard to do, as all the proxy sees is a number of discreet requests for web pages. It has no knowledge of any form of "session", and no way of knowing whether these requests are related or not.
I've never really looked into this, but expect that you may be able to estimate the time spent on a site based on your own calculations by looking at the timestamps of individual requests, and calculating the difference between the 1st and last requests you consider to be related.
You'll have to make some assumptions, though. As an example, between the time I got to your post, and the time I replied, I spent 20 minutes doing other things. You can't just assume from the 2 timestamps in a log that I spent that time on this site. At the very least I think you would have to decide on the maximum time between 2 requests that you would consider part of the same session/visit (for example 5 minutes). You probably need to take into account visits to other sites during this same time period, as some people tend to have multiple sites open at a time.
Also note that some pages may automatically refresh from time to time, even when you're not actively busy on the page (for example to load fresh ads). I often open dozens of tabs at a time for articles I want to read, and only get around to reading them hours later. The stats for such pages might not reflect reality, as it might seem like I spent hours on the site, while in reality I opened the page, left it unattended for hours, and then spent 2 minutes there to read the article.
Lastly keep in mind that in most cases there is no log entry when I leave the site (close my browser window/tab), This could skew the stats for sites with only a few requests, but is probably less significant for sites where someone spent quite a lot of time browsing around.
You might be able to find some ideas from the source code for Squint, a script which tries to report on who is spending the most time and resources browsing the internet overall via a squid proxy. It is available at
http://www.ledge.co.za/software/squint/index.php.
Good luck!
Clifford
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