The 60 day grace period is available to you for each H-1 episode whether it is an extension, amendment or a transfer. When they proposed the regulation, it was supposed to be one time 60 day grace period, but then government relented and made it available for each H-1 incident.
For some extraordinary reasons like, you got laid off without any notice and you found a job in the next 40-45 days you can apply for a transfer. You cannot start working until you have applied for the transfer, using the AC21 you can start working until the decision is made and if the decision is made and they give you concession then you can get your H-1 within USA.
Hence the 60 day period is available for each episode of H-1, two it is not automatic, you have to ask for it and three you can start working once you apply for the H-1.More...
Note: This is a verbatim transcript of the referenced audio/video media delivered as oral communication, and, therefore, may not conform to written grammatical or syntactical form.