What is This Bird?

We have an orange tree in our yard. The oranges were ripe over the winter, and now the remains of the season are falling off the tree.
I have been noticing that quite a few of the fallen oranges have holes like this one: The hole is perfectly round and quite deep. The pulp inside the hole is gone. I have seen a few Orioles struggling with my hummingbird feeder, so I assumed it must be Orioles eating the oranges. I even put up a specially designed Oriole feeder, but I haven’t seen any Orioles visit it yet.

Then, the other day, I noticed a bird high in the tree, busily eating an orange that is still on the tree. I took some pictures and realized that it’s certainly not an Oriole. The problem is I can’t figure out what it is, even with the help of some books about regional birds from the library. The identity of the visitor will stay a mystery.