Context. The recent detection of gravitational waves associated with a binary neutron star merger revives interest in interacting pulsar magnetospheres. Current models predict that a significant amount of magnetic energy should be released prior to the merger, leading to electromagnetic precursor emission. Aims. In this paper, we revisit this problem in the light of the recent progress in kinetic modeling of pulsar magnetospheres. We limit our work to the case of aligned magnetic moments and rotation axes, and thus neglect the orbital motion. Methods. We perform global two-dimensional axisymmetric particle-in-cell simulations of two pulsar magnetospheres merging at a rate consistent with the emission of gravitational waves. Both symmetric and asymmetric systems are investigated. Results. Simulations show a significant enhancement of magnetic dissipation within the magnetospheres as the two stars approach one another. Even though the magnetospheric configuration depends on the relative orientations of the pulsar spins and magnetic axes, all configurations present nearly the same radiative signature, indicating that a common dissipation mechanism is at work. The relative motion of both pulsars drives magnetic reconnection at the boundary between the two magnetospheres, leading to efficient particle acceleration and high-energy synchrotron emission. Polar-cap discharge is also strongly enhanced in asymmetric configurations, resulting in vigorous pair production and potentially additional high-energy radiation. Conclusions. We observe an increase in the pulsar radiative efficiency by two orders of magnitude over the last orbit before the merger, exceeding the spindown power of an isolated pulsar. The expected signal is too weak to be detected at high energies even in the nearby universe. However, if a small fraction of this energy is channeled into radio waves, it could be observed as a non-repeating fast radio burst.