I'm aware it wouldn't be the most historically accurate, but if I wanted to include an Ancient Era nomadic culture, I'd choose the Scythians as a more elegant solution. Although they are technically more of a Classical Era culture, the term "Scythians" is also used to refer to similar cultures of the Eurasian Steppe that existed during the Iron Age (including the Cimmerians), and so could potentially be squeezed into the first era. Not sure what the Emblematic Unit would be, but Kurgans would work again here for the EQ.
What we run into here, I think, is the fact that the "Classical" Era covers almost 1500 years (roughly, 1000 BCE to 500 CE) and so we've got succeeding Pastoral Groups:
Early Classical:
Cimmerians
Scythians - which term covers a bunch of slightly differing groups from the Ukraine to the borders of Mongolia
Xiong-Nu - which early on may have meant "anybody on a horse near China"
Late Classical:
Huns
Sarmatians
Sogdians
What makes for continuity is that once they rode horses, carried composite bows and herded, all of them shared a bunch of traits: felt tents by various names, Kurgans, Tumuli, or other large burial 'mounds', and an emphasis on Trade which made the entire steppe from China to the Danube one big Free Trade Zone, more or less.
And, I think we would be safe and saying that a lot of that probably could be 'backdated' to the late Ancient Era: kurgans certainly date back to before 3000 BCE, as do the light chariot predecessors of the horsemen in the same Central Asian steppes. I think we could safely label them Cimmerians while knowing that chronologically, we're really talking about their predecessors among the 'true' Ancient groups like the Yamnaya, Andronovo, or Afanasievo cultures.
Does BMAC count as a pastoral culture? It‘s during the heyday of Bronze Age. There are impressive city remains, but I guess most of the population would be nomadic.
The Oxus Civilization, or BMAC, is characterized by irrigated grain farming, wheeled carts drawn by oxen or camels, a number of 'city sites', but not, as far as I know, any domestication of the horse. Towards the end of the civ, after 2000 BCE, they started getting influence from their northern neighbors, the Andronovo Culture, which definitely was pastoral with horse-drawn vehicles and herds, but that resulted in a late 'integrated' culture with nomadic/pastoral elements that was not entirely BMAC any more.