I encourage you to thoroughly research your options before expecting to show up and find a job as a dive guide, particularly in Cozumel.
I can't really speak much for the other destinations, but here in Cozumel, work permits (FM3) for foreign divemasters are non-existent. If you have an instructor rating and some special qualifiers, it is possible, but not likely that you would be granted a work permit; however, they are rarely issued anymore either. Furthermore, you must be sponsored by a mexican employer, you cannot just go to the immigration office and request a permit. Finding a shop to sponsor you with your intentions of being in Mexico for the short term will prove another challenge. The island is full of Mexican nationals qualified to fill these positions, and a foreigner who wants to come work for just awhile as they travel through is not highly looked upon here. The diving industry here is highly competitive and the reality of obtaining employment as a divemaster is slim to none.
I do not mean to sound discouraging, but you should know what you are up against.
Good luck to you.