Lunula?

[Epictetus]

I can think of this passage:

Why do they that are reputed to be of distinguished lineage wear crescents on their shoes?

Is this, as Castor says, an emblem of the fabled residence in the moon, and an indication that after death their souls will again have the moon beneath their feet; or was this the special privilege of the most ancient families? These were Arcadians of Evander's following, the so called Pre-Lunar people.

Or does this also, like many another custom, remind the exalted and proud of the mutability, for better or worse, in the affairs of men, and that they should take the moon as an illustration:

When out of darkness first she comes anew
Her face she shows increasing fair and full;
And when she reaches once her brightest sheen,
Again she wastes away and comes to naught?

Or was it a lesson in obedience to authority, teaching them not to be disaffected under the government of kings, but to be even as the moon, who is willing to give heed to her superior and to be a second to him,

Ever gazing in awe at the rays of the bright-gleaming Sun-god,

as Parmenides puts it; and were they thus to be content with their second place, living under their ruler, and enjoying the power and honour derived from him?

Plutarch, Roman Questions, 76

There is also this quote that lists several other sources. They might be helpful.

In their dress and appearance the patricians were scarcely distinguished from the rest of the citizens, unless they were senators, curule magistrates, or equites, in which case they wore like others the ensigns peculiar to these dignities. The only thing by which they appear to have been distinguished in their appearance from other citizens, was a peculiar kind of shoes, which covered the whole foot and part of the leg, though they were not as high as the shoes of senators and curule magistrates. These shoes were fastened with four strings (corrigae or lora patricia) and adorned with a lunula on the top (Senec. De Tranquil. Anim. 11; Plut. Quaest. Rom. 76; Stat. Silv. V.2.27; Martial, I.50, II.29). Festus (s.v. Mulleos) states that mulleus was the name of the shoes worn by the patricians; but the passage of Varro which he adduces only shows that the mullei (shoes of a purple colour) were worn by the curule magistrates (cf. Dion Cass. XLIII.43).

Murray, Dictionary of Greek and Roman Antiquities