As anyone who's learned Sefer Melachim knows, there are a lot of places where the years of the kings of Yehuda and Yisrael don't quite seem to match up. (See this question.) As an example, Rechavam and Yeravam began their reigns at pretty much the same time, and Rechavam ruled for 17 years, but 1 Melachim 15:1 says that his son and successor Aviya(m) began to rule in Yeravam's 18th year (and in fact Radak there wonders why this should be so). There are still greater discrepancies elsewhere, for example II Melachim 13:10, which says that Yehoash succeeded his father Yehoachaz as king of Yisrael in the 37th year of Yehoash of Yehuda, and many of the mefarshim point out that the figures given earlier (that Yehoachaz ascended the throne in Yehoash's 23rd year, and reigned for 17 years) seemingly should yield the 39th year instead.
Many years ago, as a youngster, I saw an interesting book (I vaguely remember it being connected with the Mishnah about Rosh Chodesh Nissan being "the Rosh Hashanah for kings," so it might have been an appendix to a commentary on Maseches Rosh Hashanah) that goes systematically through these, and tries to explain them based on the following principles:
The reigns of the righteous kings were counted (as those of a Jewish king should be) from Nissan, while those of the wicked kings were counted like those of non-Jewish kings, from Tishrei.
Sometimes the Sanhedrin could decide to change this in the middle of the reign, if the king did teshuvah or, conversely, became wicked.
In the case of Yehoachaz, I recall it explaining (at least part of) the discrepancy as being due to the fact that he did some degree of teshuvah and "beseeched Hashem" (II Melachim 13:4), so that one of his regnal years was shortened (for example, his 16th year began in Tishrei 3098 and would have been expected to run till Elul, but instead his 17th year was considered to begin that Nissan).
The book was in English, as I recall. Hard to say about the date - I might have seen it as far back as the 1980s, but definitely no later than about 1995.
Based on all the above details, can anyone identify the book? I'd really like to read it again.