*Please motivate/introduce type I and/or type II errors.*
Having been on hiring committees at community colleges and 4-year schools, I always read the directive to "motivate/introduce" here as an opportunity for candidates to really step take a back and show how they would use non-mathematical language (first) to help students care about some new thing. This is often done through questioning them on a current event or something from the news, or a hypothetical where students are asked to bring their opinions.
In the case of *motivating* type I and/or type II errors, I think your example would be improved by having students first think about the severity of the two situations: "10% of students smoke, but we end up rejecting this" or "Some other percent of students smoke, but we don't reject the idea that 10% smoke." Yours might be a tricky example with which to do this (since it is a two-tailed test), but getting students to understand which situation could be "worse" could help them to *want* to identify these situations by name. Maybe ELAC is studying this in order to choose a plan of action -- If $H_0$ is rejected (in favor of $p$ being greater than 0.10, say), then the administration will pour resources into reducing the number of smokers. If $H_0$ is *not* rejected, then the administration will use the funds for something else needed on campus.
A question to students could be: "Which situation would you find more objectionable: There really are only 10% that smoke, but the test causes us to reject this number, and the administration pours money into helping reduce the number of smokers", or; "The percent of smokers is higher than 10%, but the test causes us to *not* reject the assumed number of 10%, and the administration saves the money for something else."
In general, I like examples like yours, but given you only have 12 minutes, I might focus on having students understand what the errors mean in context first. Then, after they could describe/identify the errors in a few different settings, explore the math involved. As for the work you plan to show, this is what I would expect of an interviewee to show us for the "follow-up" discussion. [The best interview demos begin with a here's-what-we've-done (usually just printed and handed out), then the demo, and then a where-we-will-go-next (also printed and handed out) to show the interview committee that you actually have a plan and you know where the lesson fits into the whole term.]
tl;dr version as my opinion:
Spend most of the demo on meaning first, instead of jumping to calculations.
Build your calculations into a discussion of where you would go with the class after the demonstrated material.
Make sure to develop a full plan for before-during-after the demo, and give this to the committee so they know.
Overall, keep the introduction light, meaningful and active for students. Ask them questions in plain language first, so they won't have to immediately jump a math/notation hurdle before understanding what's going on.