Well I am thinking about eventing. But I'm like GREEN. Not even broke green. I'm a complete newbie. So I don't know what I want, since I haven't actually tried anything yet.
If I wanted to find a trainer to focus on eventing, I wouldn't be able to find it in Miami. I've checked already.
If you want to get into Eventing - please look for a Coach who Rides the sport, Trains in the sport, Competes in the sport and is up to their ears in the sport. As David O'Connor and Jim Wofford say - "If your Coach doesn't piss on the pot, they need to get off the toilet" where this sport is applicable.
It is a dangerous sport, and you need a Coach who is very well rounded and involved, so that they can give you the best that they can. A Coach who not only mentally prepares you and your horse, but physically as well.
The Eventers I work with range from 3* to 4*, who they themselves take lessons. Every winter, they haul over to the O'Connors farm or the Davidson's farm to train. So the point is, regardless of the level they compete at, a good coach should still continue to educate themselves. So that when they are working with their students, they have a broad spectrum of approaches that will work for their broad spectrum of students and horses.
A good Eventing Coach doesn't push you beyond your limitations. They work with you slowly and surely to build your confidence, and your horses. They don't push you to go up in levels, nor do they discourage either. What I love about the one 3* Eventer I ride with, is that she's honest. If she doesn't think you are capeable of doing something, she's going to tell you. If she thinks you are in over your head, she'll blatently tell you. If she thinks you are in the wrong discipline, she'll tell you.
This isn't a sport to "piss" around with - from BN to 4*. A good coach will teach you respect for the sport as well.
Other aspects, have already been mentioned