While this seems straight forward, I am also imagine it not being so simple.
Let's analyze this further, fast protonation, slow cleavage of C-O bond to form water and carbocation. While water can be expected to pull proton, it could reform alcohol. Not only that, but the carbocation may have been stabilized by neighboring electrons. Could water open to give isomeric alcohol? Less likely. (I recall some labeling studies that quantized neighboring group participation, but I do not recall details.)
Deprotonation to form alkene. Reprotonation of alkene to give isomeric alcohol. Dehydration to give isomeric alkene, repeat.
I am not arguing that 4-methylcyclohexene is not the major product, but given the nature of this reaction, I should not be surprised to find small amount of isomers.