I hear a lot in songs like "The Yellow Rose of Texas" about "yellow" people, especially girls, and I know they are referring to light-skinned black/biracial people. But would Asians have also been thought of as having "yellow" skin, or would there have been a different idea as to what color they were? And were the two ever connected in any way?
I think the demographics of Texas are important to note. At the time you said, census records indicate a very negligible population of people of asian-descent in Texas. The Texas Historical Association claims it goes back to at least the 1850's as well. I can't find much reputable on the history of the term yellow, but I think its also important to point out that as minstrelsy, it was written in a faux-African American dialect. Its possible that yellow was a term for people of mixed race in that era, or it could be the way the narrator is meant to be "unsophisticated."
I'm leaning more towards it was an informal term for people of mixed race that was used with unknown commonality. The earliest I can find a sourced mention of the word yellow for the Chinese in the United States is 1874 San Fransisco. Sources:
https://texaspolitics.utexas.edu/archive/html/cult/features/0501_02/slide2.html