Aggressive track-density scaling is projected to be a key means of increasing the areal bit density and cartridge capacity in future magnetic tape recording systems. To achieve very high track densities, nanometer-scale accuracy is needed in positioning the tape head over the data tracks during read and write operations. State-of-the-art tape systems employ timing-based-servo (TBS) patterns  to estimate the head position by measuring the relative timing between sequential bursts of servo stripes. In this work, we evaluate a set of experimental TBS patterns servo-formatted on a perpendicular barium-ferrite (BaFe) tape medium and quantify the achievable resolution in the lateral position estimate. We compare closed-loop position error measurements with resolution estimates based on a) the noise floor of the power spectral density of the lateral tape motion measured from the servo pattern during closed-loop track-following, and b) an analytical lower bound which depends on the servo readback signal shape and the signal-to-noise ratio.