Magnetic reconnection can power spectacular high-energy astrophysical phenomena by producing non-thermal energy distributions in highly magnetized regions around compact objects. By means of two-dimensional fully kinetic particle-in-cell (PIC) simulations we investigate relativistic collisionless plasmoid-mediated reconnection in magnetically dominated pair plasmas with and without guide field. In X-points, where diverging flows result in a non-diagonal thermal pressure tensor, a finite residence time for particles gives rise to a localized collisionless effective resistivity. Here, for the first time for relativistic reconnection in a fully developed plasmoid chain we identify the mechanisms driving the non-ideal electric field using a full Ohm's law by means of a statistical analysis based on our PIC simulations. We show that the non-ideal electric field is predominantly driven by gradients of nongyrotropic thermal pressures. We propose a kinetic physics motivated non-uniform effective resistivity model, which is negligible on global scales and becomes significant only locally in X-points, that captures the properties of collisionless reconnection with the aim of mimicking its essentials in non-ideal magnetohydrodynamic descriptions. This effective resistivity model provides a viable opportunity to design physically grounded global models for reconnection-powered high-energy emission.