For my GP, if it is an urgent matter, I call to find out if he is in, and if so, I just go in and wait. Otherwise, I make an appointment within the week. I have never waited longer than that. He has also made evening house calls when my husband could not travel to his office, and it was not "ambulance/ER" worthy.
For my orthopedist, if I use the one at the Ajijic Clinic, it's dependent on the day of the week that he is there and his surgery schedule. Usually a week, because he is there 1x a week.
For my GDL orthopedist who is either in his office or in surgery, it depends on his schedule. For non emergencies, 1-1.5 weeks, and they will call me if there is an opening earlier.
Dentist - We schedule cleanings, etc., in advance, but in an urgent need, she will open up her office immediately. It helps that she lives in the neighborhood behind us, but I have heard the same about most dentists. For routine fillings, crowns, etc., an appointment is usually available within the week. For more complicated work that requires the assistance of an oral surgeon who will come n from GDL, usually a week.
My ophthalmologist can usually fit a person in within one week, at most 1-1.5 weeks. He does surgeries and on occasion has emergencies. I had a retinal detachment in progress and he saw me withiin 30 minutes, asking the room full of patients heading to GDL for surgery to please be patient, that he would be about 40 minutes late for all of them, but it might save my eyesight. It did. He saw me on a Friday morning and I was in surgery the next Monday morning. Had I not eaten breakfast, I would have been whisked to the eye center in GDL and operated on ahead of his cataract patients.
Hope that helps .