I have been trying to find out what was known about Castor, Pollux, beavers, etc. in the 15th-17th centuries.
The anecdote about beavers being sought after for their testicles and self-castrating themselves to avoid death, is in Claudius Aelianus's
De Nature Animalium, a Roman-era work in Greek well-known in manuscript, according to
http://www.summagallicana.it/lessico/e/ ... 20Aelianus. It was published in Latin translation in 1562, according to the title page reproduced on that site.
Alciati's book of emblems, published 1556 Lyon, has a woodcut of the beast in the act of self-castration, with a verse and the relevant excerpt from Aelianus. I take this from
http://www.emblems.arts.gla.ac.uk/alcia ... id=A56a085.

The tree in the background, a cut-off trunk, with humanoid roots and new shoots springing from it, is a standard symbol of rebirth, thus confirming my interpretation of Isadore's beaver, the "Castor," in Italian.
(People may not be familiar with this meaning of stumps. Perhaps I should digress a bit, inserting something form an old post of mine on Aeclectic (
http://www.tarotforum.net/showthread.ph ... ost2032651). In stump imagery, a branch usually grows upwards out of the top, signifying death and resurrection. Here are two examples, both from the Renaissance:

These images are from Gerhard Ladner, "Vegetation Symbolism and the Concept of Renaissance," in
Images and Ideas in the Middle Ages, p. 746 p. 746, figs. 4 and 5, at Google Books). The designation "falcon" is Leonardo's. But it looks to me more like Noah’s dove, bringing back a twig of new life. As Ladner observes (p. 733), the theme is clearly that of renewal. The branch on the stump is an image that goes back at least to Roman times: a Roman fresco found at the Villa Farnesina shows the killing of the infant Dionysus accompanied by the same motif (Ladner p. 733). And the historian Livy used the image to describe the renewal of Rome after its destruction by the Gauls (Ladner p. 731).)
Since there are many shoots in the Alciati image, it is probably a symbol for the death of Christ and the rebirth of Christians.
Here are some more historical connections betwen the Dioscori and Christianity. In
The Spaniards, an Introduction to their History, in Google books, the authors quote Mark 3:17:
"And James the son of Zebedee, and John the brother of James, and he surnamed them Boanerges, which is, the sons of thunder." Now "sons of thunder" corresponds in meaning to the Greek Dios-kuroi or "sons of Jupiter the Thunderer"...(p. 390.)
At one point James and John even ask Jesus if they should bring down fire from heaven to consume the Samaritans (Luke 9:54). Jesus declines the offer. The Dioscuri were also identified with Peter and Paul, and in Naples the church of San Paolo Maggiore was built on the site of a former temple of the Dioscuri, the columns of which still stood in the seventeenth century, with the statues of Castor and Pollux lying down behind those of Peter and Paul. In the popular imagination they were identified with the Saints Michael and George, and the medical saints Cosmas and Damian (p. 391, citing
Le Culte de Castor et Pollux en Italie[i] by Maurice Albert, 1883, pp. 47f, and the [i]Reallexicon fuer Antike und Christendom 1957, entry for "Dioscuri").
The Albert book is in Google Books, but only the first 40 pages. Another book for me to get on Interlibrary Loan. From what I have read so far, the caps can take various shapes, including Phrygian, but they are usually portrayed as ovel: they are to suggest the eggshell from which they hatched, as sons of Leda.
Here is a coin showing the Dioscuri with their caps (from
http://lab.dartmouth.edu/art2artifact/c ... sym02.html)

If the hats were Phyrgian, they would curve loosely to the side at the top.