The first direct observation of time-reversal (T) violation in the $B\bar{B}$ system has been reported by the BaBar collaboration, employing the method of Ba$\tilde {\rm n}\!$uls and Bernabéu. Given this, we generalize their analysis of the time-dependent T-violating asymmetry ($A_{T}$) to consider different choices of CP tags for which the dominant amplitudes have the same weak phase. As one application, we find that it is possible to measure departures from the universality of $\sin(2β)$ directly. If $\sin(2β)$ is universal, as in the Standard Model, the method permits the direct determination of penguin effects in these channels. Our method, although no longer a strict test of T, can yield tests of the $\sin(2β)$ universality, or, alternatively, of penguin effects, of much improved precision even with existing data sets.

11 pages, 2 figures; refs. added; reframed with expanded discussions; version to appear in PLB; Metadata abstract updated only