It was multiple wars with different groups on different sides, so it wasn't really consistent enough to be considered a single war.

In 1820, Texas was a part of the Spanish Empire. It became a Mexican state in 1821, and gained independence in 1836. In 1845, the U.S. annexed and admitted Texas as a state. The Spanish, Mexican, Texan, and American governments all initiated different campaigns at different times against different tribes. It's misleading to refer to all of these campaigns collectively as the "Texas-Indian War."

It wasn't continuous, it wasn't just one war, and it wasn't the same Indians. If you want to lump them together, you should start with Spanish colonization, which makes it much earlier.

The Apache wars lasted from 1839-1886, but it wasn't constant. The Seminole wars (in which we created a whole new Indian nation, the remnants of Creeks and other tribes plus runaway slaves) ran more or less from the War of 1812 to the Civil War, but there were lots of time-outs.

The last part of Texas' unending land-grab from the original inhabitants was against the Kikapoo, and the Texans (Confederate Army) were the aggressors. The Kikapoos were trying to get from Oklahoma to Mexico, and asked permission to cross Texas. The Texans gave them the nod, then attacked them. The survivors staggered across the border, and commenced a revenge campaign that continued until the Army's 5th Cavalry illegally crossed the border to destroy their villages. In the Movie (Rio Grande with John Wayne), the Indians were Apaches, but it's Hollywood, and nobody could spell Kikapoo.