The frequent flaring events in the X-ray and the near-IR (NIR) radiation of Sgr A∗ seem not to be periodic in time. However, statistical regularities, here termed "modulations by a pacemaker,"are found in the recorded arrival times of both types of events. The characteristic time of the X-ray pacemaker is 149 minutes, and that of the NIR pacemaker is 40 minutes. Their reality as derived from observed data can be accepted at larger than 4.6σ and 3.8σ levels of statistical confidence, respectively. These results can be interpreted as evidence for a star that revolves around the black hole (BH) of Sgr A∗ in a slightly elliptical precessing orbit, at a distance of 3-3.5 Schwarzschild radii of the BH. The period of the X-ray pacemaker, which is not a periodicity of the flare occurrences themselves, is the epicyclic period of the star orbital motion. This is the time interval between two successive passages of the star through the pericenter of its orbit. The NIR pacemaker period is the mean sidereal binary period of the star revolution. The origin of the X-ray flares is in episodes of intense mass loss from the star that occur preferably near the pericenter phase of the binary revolution. The NIR flares originate or are triggered by processes that are internal to the star. The radiation emitted in the direction of Earth is slightly modulated by the changing aspect ratio of the two components of the BH/star binary to the line of sight from Earth at the sidereal binary frequency.