Various techniques that involve switching a piezoelectric shunt have been studied for overcoming the shortcomings of purely passive piezoelectric shunts, including so-called "state-switching" (switching between short and open circuit conditions on the piezoelectric) and various forms of short-duration switching, called "pulse-switching" or "synchronized switching". Pulse-switching can be done with a simple resistor shunt, but is more effective with an RL shunt. Previous research has shown that not only can the pulse-switched RL shunt provide very effective vibration control performance, but it eliminates much of the shunt parameter tuning required by the passive shunt approach, and can be done with a simple control circuit using very little power. In addition, it has been shown that a single switched shunt can simultaneously control multiple vibration modes. This paper illustrates that switch timing is important in the performance of these systems. A numerical simulation study is presented in which the switch time and duration are varied in a multi-degree of freedom system, and the controller performance is quantified. In addition, a group of performance indices are analyzed for their potential to be used in a real-time tuning system for optimizing switch timing.