The three-dimensional electron gas is a fundamental model in condensed matter physics and quantum chemistry, and the exchange-correlation energy derived from it serves as the starting point of ab initio computations of materials. However, the wave-vector-dependent response, and hence the static local field factor G(q), has remained without accurate ground-state benchmark in the strongly coupled regime for three decades. Using diffusion Monte Carlo, we calculate G(q) and the static density-density response function across the liquid phase and find a pronounced structure in G(q) at intermediate wave vectors, already visible at metallic densities and growing with increasing interaction strength. We identify it as a fingerprint of short-range order by showing that it is required to reproduce the static structure factor. Our parametrization, valid in the entire liquid phase, predicts a low-energy resonant mode inside the particle-hole continuum.