Why are policemen called "Paco" in Chile?

Question

I already knew that in Spain we called policemen "madera" and "pitufos" due to the color of their uniforms.

Through a very popular song/hymn/chant that recently became very popular through most of Latin American countries, I came to know that in Chile (where this chant is originally from) policemen are referred in a colloquial way as "pacos".

The relevant part of the lyrics of the chant just says:

Son los pacos

Los jueces

El estado

El presidente

Understanding that this did not refer to the Franciscos or the world, I did some research and the Diccionario de Americanismos said "Pacos" are policemen in Chile:

paco

Paco de la esquina. m. Bo, Ch. Policía encargado de la vigilancia de un barrio o manzana. pop + cult → espon.

How did "paco" get to be a colloquial way to refer to police?

Answer 1

It seems that the word has been around for quite some time:

De súbito se oyó una voz que hizo dispersarse el grupo, como por encanto, y dejar solos a los combatientes.
—Allí viene el paco —dijeron, corriendo dos o tres.
Y fueron seguidos por los otros, al mismo tiempo que un policial tomó a Martín de un brazo y al zapatero de otro, diciéndoles:
—Los dos van pa entro cortitos.

This is from a text written in Chile between 1862 and 1875. As for the origin, currently the DLE says that the meaning is "of uncertain origin" (see paco⁵), but in 1992 it included the "policeman" meaning in the paco¹ article, that says that its origin is the Quechua word p'aqu 'rojizo'. This agrees with the Corominas dictionary of etymologies, that says that paco (from Quechua p'áko according to Corominas) and alpaca (from Aymara alpáka) come from the same origin, given that both languages share many words.

But how come did paco get the "policeman" meaning? The only clue I have is what the Etimologías de Chile web site says:

Es como en Chile llaman a los carabineros (policías). Esta semántica parece venir del quechua p'aku (rubio, castaño claro). Hace referencia a los ponchos castaños con los que se abrigaban los antiguos policías de Santiago (en esos tiempos llamados "serenos").

Basically, it says that the word is a reference to the color of the ponchos those policemen used to wear. If this is true, then once more it is a reference to the color of the uniform.

Answer 2

Not even carabineros know the origen of the word.

The Museo de Carabineros website has a page that try to explain it

https://museocarabineros.cl/web/sitio/reports/por-que-pacos