from Glenn's wiki link:
The Court wrote that its "precedents do not support the existence of a constitutional cause of action behind every statement a public employee makes in the course of doing his or her job." Instead, public employees are not speaking as citizens when they are speaking to fulfill a responsibility of their job.
The argument would be that Dodson is writing the book "in the course of doing his job" so he has no first amendment protection?
The two are obviously related, but the book seems separate from his job. The government is not paying him to write it, nor is it anywhere in his duties. If anything, it's within his duties as a citizen, not as a LEO, to tell his story.