I am actually currently a Brand team member for my store. I have been working for Target for roughly four years. After going to a campus recruitment event in September and inquiring about how to get into the interview process for the internship, I asked my ETL GE for my store. I applied internally through my ETL-HR and submitted my resume through eHR (where you would apply - search job listings and find the one for the ETL internship in your District/Group). You do need to have approval from your STL, ETL-HR, and your current ETL in your department. The online application (internal) will ask for your ETL's email, etc, so communicate with them about the information you need. After going through one interview with an STL at another store and going to a District interview with our DTL the following week, I received the last opening for the internship this summer. Don't let them fool you, it is definitely possible. Just keep communicating and don't let them drop it. If you want the internship, keep up with all of the information you need in order to apply and fine tune your resume. Good luck to you!
**posting on my fiance's account who also works for Target.
P.S. - I am not a business/retail studies/marketing major by ANY means - so don't feel like because you're studying something different in college that you're not a good enough applicant like I felt. I was pleasantly surprised!