Otdfbt

What were the Ethiopians doing at Thermopylae?

From Book III, paragraph XXV:

Having viewed all, the spies departed back again. When they reported all this, Cambyses was angry, and marched forthwith against the Ethiopians, neither giving command for any provision of food nor considering that he was about to lead his army to the ends of the earth; and being not in his right mind but mad, he marched at once on hearing from the Fish-eaters, setting the Greeks who were with him to await him where they were, and taking with him all his land army. When he came in his march to Thebes, he parted about fifty thousand men from his army, and charged them to enslave the Ammonians and burn the oracle of Zeus; and he himself went on towards Ethiopia with the rest of his host. But before his army had accomplished the fifth part of their journey they had come to an end of all there was in the way of provision, and after the food was gone they ate the beasts of burden till there was none of these left also. Now had Cambyses, when he perceived this, changed his mind and led his army back again, he had been a wise man at least after his first fault; but as it was, he went ever forward, nothing recking. While his soldiers could get anything from the earth, they kept themselves alive by eating grass; but when they came to the sandy desert, certain of them did a terrible deed, taking by lot one man out of ten and eating him. Hearing this, Cambyses feared their becoming cannibals, and so gave up his expedition against the Ethiopians and marched back to Thebes, with the loss of many of his army; from Thebes he came down to Memphis, and sent the Greeks to sail away.

And a little later on in

Book VII, paragraph LXIX and LXX:

The Arabians wore mantles girded up, and carried at their right side long bows curving backwards. The Ethiopians were wrapt in skins of leopards and lions, and carried bows made of palm-wood strips, full four cubits long, and short arrows therewith, pointed not with iron but with a sharpened stone, that stone wherewith seals are carved; moreover they had spears pointed with a gazelle's horn sharpened to the likeness of a lance, and studded clubs withal. When they went into battle they painted half their bodies with gypsum and the other half with vermilion. The Arabians, and the Ethiopians who dwell above Egypt, had for commander Arsames son of Darius and Artystone daughter of Cyrus, whom Darius loved best of his wives, and had an image made of her of hammered gold.

The Ethiopians above Egypt and the Arabians had Arsames for commander, and the Ethiopians of the east (for there were two kinds of them in the army) served with the Indians; they differed nothing in appearance from the others, but only in speech and hair; for the Ethiopians from the east are straight-haired, but they of Libya have of all men the woolliest hair. These Ethiopians of Asia were for the most part armed like the Indians; but they wore on their heads the skins of horses' foreheads, stripped from the head with ears and mane; the mane served them for a crest, and they wore the horses' ears stiff and upright; for shields they had bucklers of cranes' skin.

If it's not contained in books IV-VI, which I don't think it is, having read books I - halfway of VII in their entirety, the only possibility being that I somehow missed a quick reference to Ethiopia being subjected a second time, maybe could at least someone comment on the significance of Ethiopians being present in the midst of Xerxes' army?

I realize that Herodotus sometimes (maybe even deliberately?) confuses names of certain tribes… could he actually somehow be slyly referencing another tribe? This seems unlikely being that the mentioned Ethiopians are carrying bows 4 cubits long, the same as earlier mentioned.

From the Oxford English Dictionary (1928):

Ethiop

...

The Ethiopians are mentioned by Homer as a people dwelling in the far east and far west; in later Gr[eek] the name was applied chiefly to the inhabitants of Africa south of Egypt, but also to people of swarthy complexion from other parts of the world.

Under the heading for Ethiopian it further mentions that this usage is also attested in English, from the 17th century, as a generic expression for black-skinned people.

So in the quotes inquired about, the usage is likely not specifically to peoples from the area now known as Abyssinia, but rather to swarthy or black-skinned peoples.

The "Aethiopia" of Herodotus was not the same thing as modern Ethiopia. Rather, the term described anyone from non-Mediterranean Africa. At the time of the Battle of Thermopylae, the Persian Empire included part of Aethiopia, so it's not surprising that an army composed of soldiers from all over the empire would include some Aethiopeans.

As summarized in the Wikipedia article on the Second Persian Invasion of Greece, Herodotus lists 47 diverse ethnic groups which together constituted 1.7 million infantry troops, a large share of Xerces' 2.6 million forces. Whatever the accuracy of these numbers, Xerces clearly recruited soldiers from far and wide, and there may not be anything particularly special about the presence of Ethiopian ethnicities among the others.