Log event handler should support file rotation

The log event handler is very useful but the created file is never rotated so it will grow forever.

It should support file rotation via ad-hoc options.

The issue names no files, tests, or entry points, so first locate the log event handler and inspect how it handles options and writes files. Done means ad-hoc rotation options are supported and the generated log file no longer grows without bound, with the behavior covered by relevant tests.

Written by the indexing model from the issue text.