This bird is the Eastern Phoebe. When it sings, it says its name very emphatically and can be seen bobbing its tail up and down.
It is a member of the flycatcher family and, as the name implies, it eats insects. They will sit on a branch and dart out to catch an insect and then return to the branch and wait for more insects to fly by.
They migrate between the United States and Mexico, not quite to the Yucatan peninsula. And they are one of the first birds to return in the spring; all of the naturalists here wait eagerly to hear them. We all try to be the first to hear it.
Click here for a link to a very good website, All About Birds from Cornell Lab of Ornithology. It has a wealth of information. Thanks for sharing your question and pictures.
-Naturalist Denise Wolfe