Fiber ring laser gyroscopes (FRLGs) are among the most sensitive rotation sensors. Recently, we have proposed a scheme for improving the sensitivity of such gyroscopes significantly by using the fast light effect. The resulting device, called the active fast light fiber-optic sensor (AFLIFOS), makes use of a pair of counter-propagating superluminal Brillouin lasers in a fiber cavity. Compared to a conventional FRLG, the sensitivity of the AFLIFOS is expected to be enhanced by nearly four orders of magnitude. For both conventional FRLG and the AFLIFOS, the overall sensitivity increases with increasing output power. However, when the power of the pump laser used for producing the Brillouin gain exceeds a threshold value, cascaded higher order Brillouin lasing may occur, thus complicating the dynamics of the AFLIFOS, and limiting the maximum achievable sensitivity. We experimentally study the parameters that determine the onset of second- and third-order Brillouin lasing in a fiber cavity. We also analyze how the pump power affects the AFLIFOS operation and show how the measured threshold for second-order Brillouin lasing sets a practical limit for the AFLIFOS sensitivity.