The causes and consequences of among-individual variation and covariation in behaviours are of substantial interest to behavioural ecology, but the proximate mechanisms underpinning this (co) variation are still unclear. Previous research suggests metabolic rate as a potential proximate mechanism to explain behavioural covariation. We measured the resting metabolic rate (RMR), boldness and exploration in western stutter-trilling crickets, Gryllus integer, selected differentially for short and fast development over two generations. After applying mixed-effects models to reveal the sign of the covariation, we applied structural equation models to an individual-level covariance matrix to examine whether the RMR generates covariation between the measured behaviours. All traits showed among-individual variation and covariation: RMR and boldness were positively correlated, RMR and exploration were negatively correlated, and boldness and exploration were negatively correlated. However, the RMR was not a causal factor generating covariation between boldness and exploration. Instead, the covariation between all three traits was explained by another, unmeasured mechanism. The selection lines differed from each other in all measured traits and significantly affected the covariance matrix structure between the traits, suggesting that there is a genetic component in the trait integration. Our results emphasize that interpretations made solely from the correlation matrix might be misleading.