Summary: Efficient estimation of the population size from dependent dual-record system (DRS) remains a statistical challenge in the capture-recapture type experiment. Owing to the non-identifiability of the suitable time-behavioural response variation model (denoted as \(M_{tb})\) under DRS, few methods are developed in the Bayesian paradigm based on informative priors. Our contribution in this article is to develop a new integrated likelihood function from model \(M_{tb}\) motivated by a novel approach developed by T. A. Severini [Biometrika 94, No. 3, 529–542 (2007; Zbl 1134.62011)]. A suitable weight function on the nuisance parameter is derived with the knowledge of the direction of behavioural dependency. A pseudo-likelihood function is constructed so that the resulting estimator possess some desirable properties including negligible prior (or weight) sensitiveness. Extensive simulations show the superior performance of our proposed method to that of the existing Bayesian methods. Moreover, the proposed estimator is easy to implement from the computational perspective. Applications to two real data sets are presented.