With the exception of former military test pilots, who trained within their role in the military, most of the test pilots I know, were so, more because the job found them, rather than them training and looking for the job.
They were very experienced pilots first, and the testing work came along because they had the experience. Lots of hands on experience with maintenance and fabrication is vital, as well as a good grasp of the design requirements for the aircraft type involved
The training, though important, may not always be the entry point to being a test pilot, the experience and flying skill may be.I cannot imagine a civil employer sponsoring the cost of a full flight test course, for other than a very extablished employee. There are short courses, which will get you some training in chunks, and they are more affordable. From my experience, you have to be very familiar, and experienced with flight test, to get the most out of the training - it's a lot from a standing start.
Some jobs are so uncommon, that it is really hard (and/or expensive) to move yourself directly at the point of entry for that position. It does not mean that you cannot do it, but keep an open mind as to other directions from which to approach it.
In the mean time, do lots of flying, in as many differnet aircraft types as you can find. I also found it very worthwhile reading as many books on flight test, and the test pilots. What you can learn from their experience is amazng. Many of the books are listed on another thread here.
Good luck....