We summarize broadband observations of the TeV-emitting blazar 1ES 1959+650, including optical R-band observations by the robotic telescopes Super-LOTIS and iTelescope, UV observations by Swift UVOT, X-ray observations by the Swift X-ray Telescope (XRT), high-energy gamma-ray observations with the Fermi Large Area Telescope (LAT) and very-high-energy (VHE) gamma-ray observations by VERITAS above 315 GeV, all taken between 17 April 2012 and 1 June 2012 (MJD 56034 and 56079). The contemporaneous variability of the broadband spectral energy distribution is explored in the context of a simple synchrotron self Compton (SSC) model. In the SSC emission scenario, we find that the parameters required to represent the high state are significantly different than those in the low state. Motivated by possible evidence of gas in the vicinity of the blazar, we also investigate a reflected-emission model to describe the observed variability pattern. This model assumes that the non-thermal emission from the jet is reflected by a nearby cloud of gas, allowing the reflected emission to re-enter the blob and produce an elevated gamma-ray state with no simultaneous elevated synchrotron flux. The model applied here, although not required to explain the observed variability pattern, represents one possible scenario which can describe the observations. As applied to an elevated VHE state of 66% of the Crab Nebula flux, observed on a single night during the observation period, the reflected-emission scenario does not support a purely leptonic non-thermal emission mechanism. The reflected emission model does, however, predict a reflected photon field with sufficient energy to enable elevated gamma-ray emission via pion production with protons of energies between 10 and 100 TeV. ; Comment: Accepted by ApJ