Yes, slavery was the major cause of the secession of Texas from Mexico even though the slave-owning Texians were canny enough to not actually put it in writing. Anglo-American settlers from the South had been moving (or, perhaps more appropriately, illegally immigrating) to Texas for decades in order to more freely practice chattel slavery, prevent slaves from escaping into Northern ‘free’ states which increasingly refused to enforce the Fugitive Slave Acts and return escaping enslaved people back to their ‘owners’, and because of perceived coming restrictions on slave ownership by the US federal government.
I don’t know why you are so hung up on trying to ‘prove’ that slavery wasn’t an issue for the succession of Texas but there is no credible reading of the history of that era that indicates that the Texas Revolution was about any significant issue other than the continuance of chattel slavery.
Stranger