We present the analysis of James Webb Space Telescope near-infrared H2RG detectors with a 5-μm cutoff, which shows that, at temperatures <60 K, there is no measurable dark current. Instead, the observed signal in dark exposures is almost entirely due to multiplexer glow that arises as each pixel is selected. We are able to separate the per-sample glow from the time-dependent dark current by comparing the observed signal in both continuous and sparsely sampled dark exposures. Such explicit tests are required to break the degeneracy between dark current and uniform amplifier glow. We show that the glow is lower within the regions of the detector that are missing the epoxy back fill (voids). We also find that the glow from each pixel extends out to a radius of several pixels. Because of the higher sampling frequency of subarray observations, the per-sample glow leads to a higher apparent dark current in subarray exposures. Finally, we show that the magnitude of the glow is affected by the pixel source follower current, the pixel clocking rate, and the number of outputs running in parallel. Our measurement of an insignificant dark current shows that the detector noise is no longer limited by the quality of the mercury cadmium telluride layer but instead by the multiplexer and readout electronics.