If the leaving of the leaving group creates a secondary carbocation, and a tertiary carbocation has the possibility of being formed through a 1,2 methyl shift:
1) Will the methyl shift? I'm guessing the answer is an emphatic yes. Tertiary carbocations are more stable than secondary carbocations.
2) Will there still be some secondary carbocation left over? I.e. will there be both major and minor products? I'm guessing yes.
I ask because I was watching a video on E1 elimination and the narrator ignored the possibility of a shift, and I was wondering if this was because he forgot or because it was irrelevant.