Hint: This item would approximately 22"- 24" long.
THE ANSWER
Great participation once again in our quiz. The correct answer is:
And for those of you who guessed that it was an apparel for an amice, you too are essentially correct since, as our Ambrosian rite expert Nicola de Grandi pointed out, that is what the cappino essentially is; an apparel for an amice, but one now separated from the amice.
From Archdale King's Liturgies of the Primatial Sees, page 384:
The ... frigium round the neck, ornamented with a cross, are singled out for comparison. This frigium (aurifrigio), which is in fact no more than the apparel separated from the amice, is known in Milan as a cappino, and is put on after the chasuble or dalmatic, and then secured with cords.
King goes on to note:
Something similar is worn in certain of the Spanish cathedrals (collarin) and at Lyons (colletin).
Here is a view of it as worn by an Ambrosian cleric, worn around the neck at the top of the vestment, be it a chasuble, dalmatic or tunicle.
