Ah, the reason Camacho sometimes doesn't show up in Historical Mode is an oversight (which has been reported multiple times, to general silence) wherein if Mexico is Democratic (which it will be by 1940 on Historical) it is possible (but not certain) for a generic election event to override the specific one for Mexico.
The criteria for every possible candidate (noting that, regardless of anything else, no incumbent is eligible):
Francisco Múgica - Be Non-Aligned, Democratic*, or Communist. No further prerequisites.
Manuel Ávila Camacho - Be Non-Aligned or Democratic*. No further prerequisites.
Saturnino Cedillo - Complete the focus "Support General Cedillo" before he revolts. Be Non-Aligned or Fascist*.
Vicente Lombardo - Complete the focus "The Confederation of Mexican Workers". Be Democratic* or Communist.
Dionisio Encina - Have NOT invited Trotsky to the government (giving him asylum is fine) and NOT completed the focus "Communist Revolution". Be Communist, effectively requires flipping via the focus "Party of the Revolution" in order to preserve elections.
Hernán Laborde - Either have Trotsky as President already or never invite him to the government to start with (again, asylum is fine). Be Communist.
Leon Trotsky - Have invited Trotsky to the government (funny, that). Be Communist.
Jesús Degollado Guízar - Complete the focus "Legion of Christ". Be Fascist*.
Salvador Abascal - Be Fascist*. No further prerequisites.
Valentín Campa - Have Hernán Laborde as President. Be Communist.
*As mentioned above, due to a scripting oversight Mexico is not barred from generic election events, which can interfere with the special event if Democratic or Fascist (because these ideologies have generic events)
Also note, the focus "Crusade Against Atheism" does not preserve elections; the only way to flip Fascist and keep elections is the focus "Revanchist Revolution". Flipping Communist or Fascist by any means other than the focus tree will likewise not preserve elections (although flipping Democratic will).
It is possible to goozle oneself out of a candidate as Fascist Mexico but it's a bit contrived. You need to exile Calles and arrest Cedillo, so neither of them are available at any point and flipping via Revanchist Revolution leaves Abascal as the leader. Do not take "Legion of Christ" so that Degollado Guízar is not available. Since the only unconditional Fascist candidate is Abascal and he can't constitutionally be reelected, the event bugs out with a fallback "OK" option that does nothing.
Of course, the interference of generic election events is the far more pressing bug.
