Make sure you know the pattern. The most important thing for Eq.
In Eq, it's all you. They're looking at your flat work abilities, how you handle the horse, how smooth it all goes, etc. Take your time.
I like it when I see someone take their time, and really work through their pattern, and do it flawlessly and smoothly, rather than rushing through it. Make sure your position is at it's best, and your handling your horse quietly and effectively around the pattern. Work on your transitions a ton.
It's all about the smooth transitions with them.
They will probably ask you to do a quick walk, trot, canter, on the rail either before or after everyone has completed their pattern. When they tell you which gait, count to five then transition up or down. Again, think it out, don't rush it.