In the original BSG, there were "Turbo" and reverse thrust buttons on the top of the stick - that might explain some things there.
Also, we might assume that the stick, which does not presumably have a twist axis in the show (and I can't think of a real-world aircraft that has a twist stick) will roll and pitch the fighter. In most aircraft, the rudder pedals also act as brakes, so keep in mind that pedals are "multi-axis" in themselves. Although several different set-ups can be envisioned or described, it's entirely possible that rudder pedals could be employed as a throttling device. In fact, such a mechanism would direcly translate to a differential thrusting set-up, allowing the Viper to pull complex maneuvers which by means of the RCS alone might not be possible.
That said, the stick might affect the roll and pitch RCS while also delivering pitch differential thrust under certain flight limits or extremes (such as in trying to re-align the relative flight vector). Meanwhile, pedals, by using the "toe" push might induce the yaw RCS, while using the actual translation of the pedal might work on the primary throttle. In such a case, there would need to be a means of making differential thrust in yaw a conscientious consideration, and not an accidental case of not pushing hard enough on both pedals at the same time. And that's only one possible control scheme, but it does make sense if you allow it do be considered critically. If that is the case with controls, I'd want translational controls (lateral and vertical thrust) to be managed on the left console where our mystery lever is located.