Mouseflow allows you to record anonymized users journey to see where your supporters go when they're on your site. Once you've integrated with Mouseflow, you'll be given a dashboard from which you can view the user recordings.
Mouseflow also allows you to analyze specific pages. You can view heat maps to see where people are clicking, scroll maps to see how much of the page is being viewed, and view global statistics to see which pages are attracting the most user attention.
We think that this tool may be useful to get a more full understanding of the way your supporters are interacting with your site. Are your users getting stuck on one page? Are they scrolling to see the reasons for signing and updates from petition creators? Are they entering the site to sign a specific petition and then leaving right way?
One note about this service: it only shows public-facing pages, not pages that require a user to be signed in with additional permissions (including petition manage pages, though you can still see the address of the page the user was on and where they were clicking on that page.)
Another tool that records users journeys is fullstory, however this service is not anonymized.