It might be worth noting that "whisker" often carried the same meaning, according to OED.

4. The hair that grows on an adult man's face; formerly commonly applied to that on the upper lip, now called moustache, and sometimes to (or including) that on the chin (beard); now usually restricted to that on the cheeks or sides of the face. [emphasis mine]

a. pl.: usually collective; sometimes distributive, as a pair of whiskers, denoting the hair on the two sides

However, while OED asserts that what is "now called moustache" was often referred to as "whiskers" or "a pair of whiskers" (one for each side of the face), the dating attested still shows "mustache" appearing earlier.

Whisker:

c1600: My wiskers hanging o're the ouerlipp.

• Timon (1980) ii. ii. 26

1622 Some spruce yonker, with a starcht beard, and his whiskers turn'd vp.

• Mateo Alemán · The rogue; or, The life of Guzman de Alfarache (transl. James Mabbe) · 1st edition, 1622 (1 vol.).

As to why the word "mustache" made its rise in the 16th century, I can only speculate. I have no reason to believe the word grew out of any particularly notable use, like that of Shakespeare in 1598.

Regardless, other words borrowed from French (or Spanish, or Italian) have origins in the 16th century, and it would be difficult to argue that there is more significance to their appearance than the normal evolution of language.

One example is the word panache, borrowed from French.

A tuft or plume of feathers, esp. for a headdress or as a decoration for a helmet, hat, or cap. Hence also: †a tassel or other decoration resembling a plume of feathers (obs.).

1584 Like as ane hors, when he is barded haile, An fethered pannach set vpon his heid, Will make him seame more braue.

• James I of England James Vi of Scotland · The essayes of a prentise, in the diuine art of poesie · 1st edition, 1584 (1 vol.). T. Vautroullier: Edinburgh

As to why the word "mustache" made its rise in the 16th century, I can only speculate. I have no reason to believe the word grew out of any particularly notable use, like that of Shakespeare in 1598.

It would be another notch on a very long belt.

As to why the word "mustache" made its rise in the 16th century, I can only speculate. I have no reason to believe the word grew out of any particularly notable use, like that of Shakespeare in 1598.

It would be another notch on a very long belt.

It might be worth noting that "whisker" often carried the same meaning, according to OED.

4. The hair that grows on an adult man's face; formerly commonly applied to that on the upper lip, now called moustache, and sometimes to (or including) that on the chin (beard); now usually restricted to that on the cheeks or sides of the face. [emphasis mine]

a. pl.: usually collective; sometimes distributive, as a pair of whiskers, denoting the hair on the two sides

However, while OED asserts that what is "now called moustache" was often referred to as "whiskers" or "a pair of whiskers" (one for each side of the face), the dating attested still shows "mustache" appearing earlier.

Whisker:

c1600: My wiskers hanging o're the ouerlipp.

• Timon (1980) ii. ii. 26

1622 Some spruce yonker, with a starcht beard, and his whiskers turn'd vp.

• Mateo Alemán · The rogue; or, The life of Guzman de Alfarache (transl. James Mabbe) · 1st edition, 1622 (1 vol.).

As to why the word "mustache" made its rise in the 16th century, I can only speculate. I have no reason to believe the word grew out of any particularly notable use, like that of Shakespeare in 1598.

Regardless, other words borrowed from French (or Spanish, or Italian) have origins in the 16th century, and it would be difficult to argue that there is more significance to their appearance than the normal evolution of language.

One example is the word panache, borrowed from French.

A tuft or plume of feathers, esp. for a headdress or as a decoration for a helmet, hat, or cap. Hence also: †a tassel or other decoration resembling a plume of feathers (obs.).

1584 Like as ane hors, when he is barded haile, An fethered pannach set vpon his heid, Will make him seame more braue.

• James I of England James Vi of Scotland · The essayes of a prentise, in the diuine art of poesie · 1st edition, 1584 (1 vol.). T. Vautroullier: Edinburgh