This article might be helpful or interesting, concerning timing: https://www.nytimes.com/2011/08/21/magazine/do-you-suffer-from-decision-fatigue.html
My daughter had a couple of experiences when going first was not the best thing, however, and both times had to do with the panel not being early-morning people. Her college audition for the place she eventually went (and did very well) was at 7:30 am and the teacher leading the audition (who became her wonderful teacher for four years in the end) actually got her name wrong and asked for a Bach movement by name that was not on her program. She was so thrown, at 17, that she played under-par and ended up on the waitlist. The story had a happy ending, but she’s not a morning person and neither is he (nor probably anyone else on that panel.) For a precollege audition (one she didnt make) she was also first of the day and several key members of the panel did not even hear her play. I saw them get off the elevator and stand in the hallway clutching Starbucks cups while she was playing on the other side of the door. So, I wouldn’t pick the first slot if it’s early morning when auditioning for a panel of musicians.