To google a spanish group, you need to put the noun first, such as "Organizacion Emiliano Zapata Campesino" (and change English spellings, such as substituting a 'c' for the 'z' in organization).
This is probably a splinter or sub-group of the
Ejercito Zapatista de Liberacion Nacional (EZLN or Zapatista National Liberation Army). (This link is a quick overview of the group, written, improbably, as part of a site designed for Irish people to learn about events in Mexico.)