We study the beta-relaxation dynamics for liquid metal gallium using computer-simulated liquid structures in conjunction with idealized mode-coupling theory. At the dynamical transition point, our calculated modecoupling parameter lambda is numerically more consistent with the increasing trend of the magnitude of the experimentally fitted lambda (similar to 0.8) observed in several glass-forming materials. The implication is that the empirically fitted lambda inherently must contain contributions arising from other subtle mechanisms to the beta-relaxation dynamics in addition to the usual cage-diffused mechanism. Of particular interest in our calculations is the behavior of the tagged particle distribution function, which shows a distinct double-peaked structure and, within the beta-relaxation time regime, exhibits a much slower retarded motion compared with other simple monatomic systems. This curious behavior is interpreted here as due to the influences of temporally fluctuating atomic bonded-pair clusters that have been observed recently in molecular dynamics simulations.