Radiation detection systems for security applications are often equipped with neutron sensors and required to promptly respond with an alarm if the neutron flux exceeds the background level. As the ambient neutron flux is essentially caused by cosmic radiation, this background could be evaluated by assessing the rate of muons crossing the gamma-ray detector which is comprised in such systems anyway. A study performed with a commercial Backpack Radiation Detection System (BRD) demonstrates the feasibility of this approach, supposed the gamma spectrometer is capable of discriminating muon signals from energetic events caused by the gamma-ray cascades following neutron captures. This requires a dynamic range exceeding the usual 3-4 MeV. The instrument used provided standard spectroscopy up to 10 MeV and facilitated charge-loss compensated spectroscopy up to 1 GeV, which allowed a separate assessment of normal gamma events (< 3 MeV), neutron-capture gamma events (3-7 MeV), and muon events (> 10 MeV). In this case, the rate of neutron-capture gamma events can be used as a neutron indicator on its own, while the muon rate signals the ambient neutron background level.