In this paper, we report a detailed experimental investigation of sedimentation of a sphere through wormlike micellar fluids by a combination of rheometry, particle tracking velocimetry, and particle image velocimetry techniques. Beyond a critical threshold, a sphere never reaches a terminal velocity and instead exhibits oscillatory motion in the axial direction similar to previous reports [ Jayaraman and Belmonte, Phys. Rev. E 67, 065301R (2003); Chen and Rothstein, J. Non-Newtonian Fluid Mech. 116, 205-234 (2004)]. Although this phenomenon has been reported in the past, there is little understanding of how various parameters affect sphere motion and whether it follows any scaling laws. In this work, we systematically varied parameters such as sphere density, sphere size, temperature, and concentration of surfactant and salt for the cetyltrimethylammonium bromide/sodium salicylate system over a wide range of inertia and elasticity. It is shown that a Deborah number, defined here as characteristic shear rate ((gamma) over dot = (V) over bar (s)/d, where (V) over bar (s) is the average terminal velocity and d is the sphere diameter) multiplied by the relaxation time (lambda), is insufficient to quantitatively characterize the onset of oscillatory motion. However, a locally determined extensional Deborah number based on the maximum strain rate multiplied by the relaxation time (De(ext) = lambda(epsilon) over dot(M)) presents a suitable criterion to separate different modes of sphere motion (i.e., unsteady and steady) in a phase diagram. Our results indicate the importance of the extensional flow in the wake of spheres as the main mechanism for the sphere instability in wormlike micellar solutions. (C) 2016 The Society of Rheology.