Actually many of the tasks (test points) performed by the test pilot can be very dull and are best done by the autopilot.
I don't know about the autopilot, but yes, much of test flying is very dull and mundane. The only reason that dull and mundane is not easy, is that immense precision of hitting the test point right on is still required.
I have noticed which flying under mentoring from formal test pilots, and in some cases, flying right seat PIC to a formal test pilot flight test, is that the best test pilots are "unconsciously competent" at simply flying the plane. The flying part has to just "be there", so that the actual objective of the flight is foremost in what's going on. I have, as the sole test pilot, sometimes have just needed a few hours of building the competence with a new type, before actually flying it for the purpose of demonstrating design compliance. In defense of a couple of formal authority test pilots, for whom I have taken the role as pilot not flying PIC, I can see that they've been thrown into the deep end. Indeed, on one program, I was satisfies that the authority test pilot was so far away from that class airplane experience, that he could not have landed it safely at all. Finding that out in flight sets up some awkward cockpit dynamics! More recently, I have found, that while flying right seat PIC to an authority test pilot in a client's plane, I've been asked [told] that only I may land and take off, not the other pilot. I agreed with a quiet inside voice relaxation.
I, as a few of my test pilot mentors over the years, came to test flying by being the most experienced pilot for the type, who was available to fly the program. I did not come to it by enrolling in a flight test course first. So, my career has a glass ceiling, as most organizations require formal training early on, to go on to the top of the profession. I'm quite happy not going on to greater heights in flight testing, I've accomplished a lot already. I took task specific flight test training along the way, but not in a formal flight test "school", I hired qualified instructors to teach me specific flight test tasks, appropriate to what I was testing. In part, because most of what I test fly (float and ski installations and external probe/camera installations, and taildraggers) is not really taught in flight test schools much.
I can't speak much to the FTE role, as I do little of that. I have hired a few from time to time. Ultimately, I have seen that experience, and unconscious competence with the aircraft, are what the employers are looking for. Happily, I came to flight testing with thousands of hours in various GA types, and sought only to flight test that class.
If you want to be involved in flight testing, my first, and best advice, based upon my life of doing it, is to be where it is happening, and make yourself useful and dependable there in any role, as you learn the skills, and build the confidence of the people around you. Then keep working at it, and as time passes, you'll rise. If you stay long enough, you'll be known as the dependable person they know that they need for the job.