The article suggests that a sauce pan should be used, but the pictures show a saute pan. Is it better to have a shallow pool or deep pool of syrup?

I think the important thing to remember is that it should not be a reactive pan (i.e. cast iron frying pan, etc.). A sauce or saute sized pan is only relative to the amount you are preparing. You do not want the mixture spread too thinly in the pan as it could heat up too quickly, and the temperature is harder to control. If you are making a smaller amount, use the smaller pan. Remember the bit about the induction or electric stove as opposed to gas. Apparently gas flames are more variable than induction or electric for the preparation of this mixture. Control of the application of the heat is paramount. It should be steady and constant.