I've decided to quit academia and am actively looking for other employment. Colleagues of mine have kept their postdoc advisors close as they've looked for work, but they also had close relationships with their advisors (maybe their advisors even helped out).
My advisor is only really interested in whether I'm producing a paper, so I don't see any real reason to give more than the standard 2-week/month notice once I've found a position. That is, unless there's some academic standard practice.
What's "good practice" in terms of notification?