Keep eye contact with that person specific and consistent. When doing two or more pieces, find the order that makes you comfortable . Try them both ways and find out which way feels best to you. Then, consistently rehearse them in the chosen order. Rehearse your transitions from introduction to character and in and out of characters ahead of time.
Transitions are the place where most actors fall apart.
There are different approaches to transition breaks, but whatever you choose to do, make sure that yours are rehearsed. Rehearse, rehearse, rehearse. Show the piece to as many people as possible. Even if you are working with a coach, get others to watch you. The more comfortable you are doing the piece, the more comfortable you will be at the audition.