"go to town on his pinkie finger"

Reading at the moment over the webpage of cnn.com/health section, I found out the below line I have a confusion making me think about the right understanding. Would you please give me a hand? Thanks in advance.

"Even if your baby is solely breastfed, your husband can get involved by adding the finishing touches. When she's done dining, your partner can let the baby go to town on his pinkie finger for a few minutes."

(go to town, I looked it up in the dictionary though I can not connect this with the following phrase, on his pinkie finger.) What does the phrase mean?

ANSWER: "Go to town" means to do something with gusto; to do something with great speed and energy (rapidly and efficiently). "Pinkie finger" (ca. 1808) means the fourth and smallest finger of the hand or simply the little finger.

Thus, what is meant is that when the mother finishes breast feeding the baby, she can give the baby to the father and the father can let the baby suckle his little finger, and the baby will naturally do so with vigor, at least until he/she realizes there is no milk coming forth. And also, if the baby is already satiated (satisfied or full), it is unlikely he/she will suck the little finger. I hope this helps. "Ambiguous Bill"