I am a graduate of Boy's State, one of my sons also graduated from Boy's State and I am now in my second year as the county Boy's State coordinator for the American Legion as well as a trustee to our State's Boy's State Foundation. Thus you might infer that I know something about Boy's State.
Some thoughts, Each Legion Post does the process their own way and the interviewers might look for different things BUT
1. A desire to learn about government
2. Some thought of serving your community and nation
3. Express interest in what Boy's State is about and doing the extra effort to run for offices
4. Be respectful of the Legionairre's service whether it was 1 or 30 yrs (they might or might not tell you)
5. Be mindful that the Legion incurs a significant expense to put on Boy's State because they want the next generation (yours) to have a chance to really understand our system of government.