The earliest references to anilingus or "ass-licking" that I am currently aware of literally predate Mozart by over two thousand years. Namely, the ancient Athenian comic playwright Aristophanes (lived c. 446 – c. 386 BCE) probably alludes to anilingus in a couple of his surviving comedies.

In his comedy Ekklesiazousai or Assemblywomen, which was first performed in Athens in around 391 BCE, the main character Praxagora has the following conversation with her husband Blepyros, in lines 646–648:

Πραξάγορα: "πολὺ μέντοι δεινότερον τούτου τοῦ πράγματός ἐστι,"
Βλέπυρος: "τὸ ποῖον;"
Πραξάγορα: "εἴ σε φιλήσειεν Ἀρίστυλλος φάσκων αὑτοῦ πατέρ᾽ εἶναι."
Βλέπυρος: "οἰμώζοι γ᾽ ἂν καὶ κωκύοι."
Πραξάγορα: "σὺ δέ γ᾽ ὄζοις ἂν καλαμίνθης . . ."

This means, in my translation:

Praxagora: "It would be far worse, though, if there were this occurrence."
Blepyros: "What sort?"
Praxagora: "If Aristyllos were to kiss you, claiming that you are his father."
Blepyros: "If he does, he'll at least wail and shriek!"
Praxagora: "But you at least would smell of calamint."

The last line here is a pun; the word "καλαμίνθη" means "calamint," which is a kind of aromatic flowering plant, but the second part of the word sounds like the word "μίνθος," which means "shit."

In Aristophanes's other comedy Ploutos or Wealth, which was originally performed in 408 BCE, but only survives in a later revised version that Aristophanes made sometime around 388 BCE, the members of the chorus threaten the enslaved character Karion, telling him, in lines 313–315:

"μινθώσομέν θ᾽ ὥσπερ τράγου
τὴν ῥῖνα: σὺ δ᾽ Ἀρίστυλλος ὑποχάσκων ἐρεῖς,
ἕπεσθε μητρὶ χοῖροι."

Which means, in my own translation:

"We will smear your nose with shit, just like that of a goat,
and you, a half-gaping Aristyllos, will say:
'Follow your mother, piglets!'"

Once again, the last line here is a pun; the Greek word "χοῖρος" literally means "piglet," but was commonly used in Attic Greek as a vulgar slang word meaning "vulva," roughly equivalent to the English word "pussy."

In both of these passages, the joke is evidently that Aristyllos has some kind of sexual fetish involving feces. Daniel Christopher Walin argues in his 2012 doctoral thesis Slaves, Sex, and Transgression in Greek Old Comedy, on page 100, that Aristophanes is most likely specifically implying that Aristyllos enjoys performing anilingus, although he notes that other commentators "are not generally so specific."

Walin is most likely correct in this interpretation, since the passage in Wealth describes Aristyllos as having fecal matter smeared all over his nose and his mouth "half-gaping," which fits very well with the anilingus interpretation.

This is a fun one, as some answers have already shown. However, Mozart's song is in specific reference to an event we can more or less confidently date to about 1515, as it was recalled and written in the memoirs of notorious one-armed robber knight Götz von Berlichingen.

Mozart likely heard the story through the popular play about him written by Goethe in 1771. Using Götz as an archetype of liberty in a time of political tyranny, the play was a popular success, and helped to popularize several of Götz’s more colorful moments, such telling Marx Stumpff to lick his ass. The phrase earned immortality as the “Swabian Salute,” and the play Götz von Berlichingen is considered one of the foundational texts of the Sturm and Drang movement in German drama. The movement’s emphasis on freedom, emotion, and human agency was intended as a counterpoint to the increasingly dominant ideology of rationality brought on by the Enlightenment.

Unfortuntely I don't have my copy of the play to hand, but I can give the full scene as presented in Götz' memoirs. This occurred in 1515, when Götz was involved in a feud with the stift - sort of a leased property - of the Bishopric of Mainz. Götz’s feud was triggered by the forceful abduction of at least one of his tenants in order to work land that was claimed to be a part of the Stift of Mainz, by men who lived in the village of Buchen. In seeking recompense for the use of Götz’s tenant, he pursued not only the authorities of Buchen, but also the Bishop of Mainz, the - absentee, in this case - landlord of the Stift. When no agreement could be arranged between Götz and those he deemed responsible for the insult to his tenants, Götz then formally declared a feud by sending the Bishop an Abklag, a written, formal opening to the feud.

At one point, Götz had taken one of the men of the bishopric prisoner and held him for ransom in a castle, until a Marx Stumpff, a fellow poor knight, had betrayed the man's whereabouts and facilitated his escape. Götz notes that Stumpff must have earned his office at Krautheim behind the deal. He continues:

Now I was of a mind that I should bless this land further, and try to push my luck, and I wanted a bit of revenge. One night I burned three places: Ballenberg, Oberndorf, and the sheep house at Krautheim, there at the bottom of the hill beneath the castle, so close that you could talk, either up to the castle or down from the walls. I didn’t like to burn things, but I did it this time thinking that Stumpff, the Amtmann (a sort of appointed man, a reeve or bailiff), would come to the fire. I waited there for an hour or two, between Krautheim and Neuenstetten, until it grew light, and over the ground lay a light dusting of snow, hoping that I might run into him. Then he called out from above, toward Klepsen, and there I called up to him that he should lick my ass.

So, Götz, having found where Stumpff was now an Amtmann at the castle of Krautheim, decided to try to lure him out by burning several buildings in nearby villages. Stumpff evidently didn't take the bait, but came to the walls in the morning to see what was going on, and had a brief exchange with Götz, who invited him to lick his ass.

Goethe rendered a similar scene, which is likely what Mozart based the song on. All translations of the memoir above are mine.