I used Timeneye by the past (free tier, personnal use), and it was neat. I need a solution which works with Trello, and they provide a browser plugin to do so. Then I switch back to Firefox, for which they don't have plugin, for now. So I moved to Toggl (still free tier), which is nice, but does not suit my needs as good as Timeneye did.
"https://www.timeneye.com/" Could work? There's no specific 'feature' for it but if you were to make a task called 'Interruptions' it'd be one way round it. Timeneye makes graphs and reports from all the times recorded. They also has a free app for your mobile or you can get it as a browser extension so it's one click away. That would help with discretely setting the timers. Hope this helps :)
I am using Timeneye time tracking - it seamlessly integration with Basecamp and Google Calendar. Basically I just need to comment my to-dos with with the time spent on them and they will be automatically added to my time entries. When I want to directly track the time I spent for a task in real time I usually start timers directly from Timeneye dashboard (https://www.timeneye.com/).