It may predate Hitler, it doesn't predate the Roman Republic
Apart from what was pointed out, does anyone actually know if there's some tradition about Mexican presidents being sworn in that dictates or suggests something like this?
Yes, see
https://en.wikipedia.org/wiki/President_of_Mexico
"Oath of office[edit]
"
Upon taking office, the President raises his/her right arm to shoulder-level and takes the following oath:
"Protesto guardar y hacer guardar la Constitución Política de los Estados Unidos Mexicanos y las leyes que de ella emanen, y desempeñar leal y patrióticamente el cargo de Presidente de la República que el pueblo me ha conferido, mirando en todo por el bien y prosperidad de la Unión; y si así no lo hiciere que la Nación me lo demande."
(My emphasis - the translation of the oath is @ the URL above)
&
presidente doesn't need an accent, the accented syllable falls naturally (by Spanish phonic rules) on the second-to-last syllable. Good work getting the correct accent into the title, though.
As for the salute - people reciting the US Pledge of Allegiance before 1942CE or so gave a similar salute, as memory serves. See
https://en.wikipedia.org/wiki/Pledge_of_Allegiance
"Salute[edit]
"Children performing the Bellamy salute to the flag of the United States, 1941.
"Swearing of the Pledge is accompanied by a salute. An early version of the
salute, adopted in 1887, known as the Balch Salute, which accompanied the Balch pledge, instructed students to stand with their right hand outstretched toward the flag, the fingers of which are then brought to the forehead, followed by being placed flat over the heart, and finally falling to the side.
"In
1892, Francis Bellamy created what was known as the Bellamy salute. It started with the hand outstretched toward the flag, palm down, and ended with the palm up.
Because of the similarity between the Bellamy salute and the Nazi salute, which was adopted in Germany later, the US Congress stipulated that the hand-over-the-heart gesture as the salute to be rendered by civilians during the Pledge of Allegiance and the national anthem in the US would be the salute to replace the Bellamy salute. Removal of the Bellamy salute occurred on December 22, 1942, when Congress amended the Flag Code language first passed into law on June 22, 1942.[33]"
(My emphasis - more @ the URL)
& so it goes ...