  We formulate a semiclassical approach to study the dynamics of coherence loss
and revival in a Bose-Josephson dimer. The phase-space structure of the
bi-modal system in the Rabi, Josephson, and Fock interaction regimes, is
reviewed and the prescription for its WKB quantization is specified. The local
density of states (LDOS) is then deduced for any given preparation from its
semiclassical projection onto the WKB eigenstates. The LDOS and the non-linear
variation of its level-spacing are employed to construct the time evolution of
the initial preparation and study the temporal fluctuations of interferometric
fringe visibility. The qualitative behavior and characteristic timescales of
these fluctuations are set by the pertinent participation number, quantifying
the spectral content of the preparation. We employ this methodology to study
the Josephson-regime coherence dynamics of several initial state preparations,
including a Twin-Fock state and three different coherent states that we denote
as 'Zero', 'Pi', and 'Edge' (the latter two are both on-separatrix
preparations, while the Zero is the standard ground sate preparation). We find
a remarkable agreement between the semiclassical predictions and numerical
simulations of the full quantum dynamics. Consequently, a characteristic
distinct behavior is implied for each of the different preparations.
