Did you work for Target before being the Closing TL? I would say what made me successful in that role was really be outgoing with everyone. Really taking the time to get to know EVERYONE in every work-center and saying "hi" all the time. That way when you are checking in, it won't seem out of place, if maybe the reason you're checking in is because their work output is lacking or they're being otherwise derelict.
Build strong partnerships with your peers. Listen to what challenges they have so you can help support them. Be really communicative with your management to let them know what you're seeing at night, and what challenges you're facing so that you can proactively tackle problems. Don't give them an opportunity to see bad closes, and blame them on you. Instead, they should see that you had a night with challenges, but these were the actions you took to mitigate and fix them.
If you have any other specific questions, feel free to ask.