The first time I saw al pastor turning on a spit, I flashed back to when I was in Sydney Australia and frequented Turkish shops for their delicious Doner kebabs. The meat cooked on a vertical spit and they trimmed the meat off as it turned. While al pastor can be cooked in a pan, it is traditionally cooked on a vertical spit, in much the same way as Doner meat.
The breaking up of the Ottoman Empire took place over a large span of time, between 1792 to 1923. Today, what is left, is known as modern day Turkey. After the Ottoman Empire broke up, a large number of Lebanese, Syrians, and Palestinians immigrated to Mexico. The Lebanese immigrants brought with them their rotisserie method of grilling meat on a vertical spit. In Lebanon, these spits had been used primarily to grill lamb, in Mexico they used them to grill pork. This is how al pastor came to be grilled on a vertical spit.
What I have written above is merely a representation of what I have read on Wikipedia and understood from what has been collected there. I do not claim to be a historian. Below are links to some of the pages I read from for those that are curious about where I got my information or would like to learn more.
Dissolution of the Ottoman Empire
Arab immigration to Mexico
Al pastor derived from shwarma
The pictures below were also taken from Wikipedia
Doner kebab: http://en.wikipedia.org/wiki/Doner_kebab
Al pastor: http://en.wikipedia.org/wiki/Al_pastor