Recent longitudinal research using the random-intercept cross-lagged panel model (RI-CLPM), which disentangles the within and between variances, has afforded greater insights than previously possible. Moreover, the impact of reading enjoyment and reading for fun on subsequent school achievement, and vice versa, has only recently been scrutinized through this lens. This study's longitudinal data (grades 3, 5, 7, and 9) comprised 2,716 Australian students aged 8 to 16 years, with school reading achievement measured by the National Assessment Program: Literacy and Numeracy (NAPLAN). The RI-CLPMs' within-person effects were not trivial, accounting for approximately two-thirds and one-third of the variance in enjoyment/fun and achievement, respectively, with between-person effects accounting for the balance. Here, we highlight a reversing direction of reading achievement's cross-lagged effect on subsequent reading enjoyment but note that the evidence for this over a reciprocal directionality was marginal. In mid-primary school, achievement at grade 3 predicted enjoyment at grade 5 more than the converse (i.e. enjoyment at grade 3 to achievement at grade 5). By secondary school, however, the directionality had flipped: enjoyment at grade 7 predicted achievement at grade 9 more so than the reverse. We termed this pattern the skill-leisure-skill directionality (S-L-S), as it concurred with the only two former studies that modelled equivalent instruments with the RI-CLPM. This model's cross-lagged estimates represent deviations relative to a student's average (i.e., within-person effect). In other words, students who enjoyed reading more (or less) in grade 7 achieved reading scores that were higher (or lower) than their average in grade 9. The implications for reading pedagogy are further discussed.