I am browsing through Nacimientos, Defunciones of years 1878 - 1880.

And when it starts at 1880 page 23, from page 24 to end of book, "Calixto Madera's signature is on every page and it seems that he is signs his name and records the information for couples that are registering the birth of their baby.

https://familysearch.org/pal:/MM9.3.1/TH-1942-21320-19588-18?cc=1918187…
https://familysearch.org/pal:/MM9.3.1/TH-1942-21320-19548-94?cc=1918187…

If you read through every page, "Calixto Madera's signature is in all of them.

Was he an employee at the Civil Registration or a witness for the couples registering the birth of their baby?

My Great Grandfather Calixto Madera was born in the early 1850's around 1856. His parents are Patricio Madera/Maria Dimas De La Paz.

Soy by 1880, My Great Grandfather Calixto Madera would be around in his early or mid 20's.