Couch's Kingbird, Clay-colored Thrush
Here is a photo of the woodpecker:
I will need a Mexican field guide to identify this more precisely.
We saw the following bird later that afternoon after we had returned to the Club Med. It was flitting around in a brush pile near the resort.
Here is a second photo of the same bird a few minutes later:
Perky little fella! I have no idea what it is called at the moment.
Here is a table summarizing the day's observations.