Localized structures (LS) in lasers have been actively sought for all-optical information processing. So far, two distinct approaches have been developed for achieving LS: one leading to addressable stationary peaks of light in the transverse section of the resonator, the other leading to addressable mode-locked pulses having a fundamental mode spatial profile. Here we show that temporal localized patterns appear in nearly self-imaging Vertical External-Cavity Surface-Emitting Lasers (VECSELs) with an intracavity saturable absorber. The observed patterns consist of a combination of an axial plane-wave with a set of tilted waves having a hexagonal arrangement in the Fourier space. In the time domain these patterns are individually addressable mode-locked pulses having a duration of about ten picoseconds. The theoretical analysis shows that the emergence of these pulsating patterns is a signature of a Turing instability whose critical wave vector depends on spherical aberrations of the optical elements. Our result shows that large aspect-ratio VECSELs offer unique opportunities for studying spatio-temporal phenomena and it paves the way to the generation of spatio-temporal LS.