The song is traditional.
Cancionero folklorica de Mexico, volume 1, Coplas del amor feliz, verse no. 2248, p. 297, provides one verse and in a footnote lists places of collection, publications (including Hague), and recordings. Borras is not mentioned.

Tecolote de guadaña
pajaro madrugador,
quien tuviera alitas
para ir ver a mi amor

The various titles applied to the piece also are given.
The first reference given is to a collection, Conc. Bajio.

As "El tecolote," found in Oaxaca, Michoacán, Federal District, in oral tradition (Emphasis mine). Other collections are listed.

As noted in a previous post, it is known in New Mexico and the SW U. S.

SACM, the Mexican Society of authors and composers, gives his birth date as 21 April, 1907, a brief biography, and a list of 20 of his compositions. Of course he arranged many pieces, and El tecolote may have been one of them.
The biography lists 20 of his compositions, none about the owl.

Sorry about the lack of accents; I don't have my HTML symbols handy.