Examples of “southern American literature and music” that features mockingbirds include Hush, Little Baby, Listen to the Mockingbird, and To Kill a Mockingbird, in case non-Americans were wondering.
The rationale for Texas in particular to choose M. polyglottos as its state bird was apparently that 1. it is familiar and found in most biomes, 2. “is a singer of distinctive type”, and 3. (because you don’t mess with Texas) fights to the death in defense of its territory.
Personally, though, I think there were lots of more unique choices, some of which will be featured in factsheets very soon.
Factsheet illustration is from the second volume of American Ornithology, or the Natural History of the Birds of the United States (1810) by Alexander Wilson and is public domain.