Example given in book is 2-methylcyclopentanol. (for ease of visualization: cyclopentane, top carbon alcohol, adjacent carbon has methyl)
Which is the product?
Answer is C.
I do not need help with this question; I understand it perfectly. Rather, a modified version of this question.
What if we gradually lower the temperature of this reaction. Which other products could E1 produce? (ignore E2's, and SN1/2's)
What I think: In addition to the product above, the carbocation shifts to the tertiary carbon. Then elimination can occur with product A as well. But, C is still major product.
Right?
Which is the product?

Answer is C.
I do not need help with this question; I understand it perfectly. Rather, a modified version of this question.
What if we gradually lower the temperature of this reaction. Which other products could E1 produce? (ignore E2's, and SN1/2's)
What I think: In addition to the product above, the carbocation shifts to the tertiary carbon. Then elimination can occur with product A as well. But, C is still major product.
Right?