I think Malachi's point is well taken, and I use a specific trigger point myself, most of the time. However, the original poster referenced Masters of the Bare Bow. I don't know if he was specifically referencing Rod Jenkins's section, but Rod does not use a specific trigger point. Instead, the release suggested by Rod is to initiate the expansion phase and then increase back tension until the shot goes off. The last cognitive thought of the shooter is to initiate the expansion phase of the shot, and then his job is simply to increase back tension until the shot goes off at some point during that cycle. Since the shooter is not cognitively triggering the shot, it is a surprise release. Because there is no specific triggering event, when this method is taught it is common to omit the "release" from the steps that need to be taken to shoot a shot. In Rod's method, for example, he lists balanced holding, expansion, and conclusion as being the three final steps of the shot process, without including release as a separate step.
There are really two potential problems with releasing the arrow without a specific triggering event:
1. Some people will expand until they get blue in the face without the shot "just going off."
2. Some people who are initially able to achieve a surprise release without any specific triggering event will develop target panic and eventually will feel compelled to release the arrow prior to entering the expansion phase of the shot.
Other people, including some of the top shooters such as Rod Jenkins and Rick Welch, are able to successfully have a surprise release without using a specific triggering event. Rod's release occurs at an undefined point during the expansion phase, while Rick's occurs at an undefined point while he is holding at full draw. So you have several different options to choose from, depending on what works best for you.