Predicting major product of a reaction with nitrous acid $\hspace{4.5cm}$

For the above reaction I am asked to predict $\ce{X}$, the major product.

Of the options given, I thought product (1) would be correct, seeing as how it has the most stable intermediate cation (tertiary) and a highly substituted double bond.

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The answer however states that product (2) is the major product.

I can't understand why the second product would be favored over the first. There's no obvious stabilizing factor here in product (2).
I think (2) is correct, but either your or your book erred in writing it. This is what the mechanism (and major product) should be: