For example:
http://localhost:8080/job/frog/11/console?elapsed=01:21

...could open the console at the line that was logged 1 hour 21 minutes after the build started.

It is already possible to add anchor names into the time-stamp format, but this has several drawbacks:

• There is no way to differentiate between multiple lines with the same time-stamp.
• When opening the link, the breadcrumb bar appears on top of the target line.
• Not all lines are displayed at the /console URL, and so some anchor links have no effect unless using the /consoleFull URL.

Perhaps an offset could be used to distinguish between multiple lines with the same time-stamp, e.g.
http://localhost:8080/job/frog/11/console?elapsed=01:21
http://localhost:8080/job/frog/11/console?elapsed=01:21+1
http://localhost:8080/job/frog/11/console?elapsed=01:21+2

Raised in response to JENKINS-21171.