We have experimentally studied the distribution of the spatial extent of modes and the crossover from essentially single-mode to distinctly multimode behavior inside a porous gallium phosphide random laser. This system serves as a paragon for random lasers due to its exemplary high index contrast. In the multimode regime, we observed mode competition. We have measured the distribution of spectral mode spacings in our emission spectra and found level repulsion that is well described by the Gaussian orthogonal ensemble of random-matrix theory.