In E1 reactions, does carbocation stability have impact on the final product?
The answer above only shows one of the two possible isomers that could be formed by elimination from the tertiary carbocation intermediate.  



I suspect that both isomeric cyclohexenes with tri-substituted double bonds would probably be produced in roughly equal amounts, along with a smaller amount of the exo-methylene compound.

Edit:  Thanks to Bon and Yolo123 for their comments

Elimination towards the isopropyl group is also a possibility, but two factors argue against this being the major elimination pathway.  First there is a statistical factor;  there is only proton on the central isopropyl carbon available for elimination, whereas the are 4 (2+2) protons available alpha to the carbocation center in the 6-membered ring.  Second, if you look at a model and consider that the proton to be eliminated must be lined up with the carbocation p-orbital you see that each methylene group adjacent to the carbocation has one hydrogen well lined up for elimination, whereas to properly line up the isopropyl proton results in some adverse steric interactions between the isopropyl methyl hydrogens and the ring methylene hydrogens.  

My guess is that the gem-dimethyl group in the cyclohexane ring will not favor one in-ring elimination pathway over the other - my model doesn't show them exerting any adverse steric effect one way or the other.