[WarZone] It seems more plausible that a foreign operative or an operative working on a foreign government's behalf might have been able to install an antenna/sensor apparatus onto the top of a structure that is part of the facility and within line-of-sight of the valley below without anyone noticing. This could allow them to persistently gather electronic intelligence on whatever might be happening on, around, and over White Sands and at Holloman. With the capabilities of modern electronics and batteries, it's possible that such a system wouldn't even need to be hard wired.
For instance, check out this 360 photo of a publically accessible viewpoint and weather station adjacent to the main solar telescope tower up at Sacremento Peak. The small building is covered with antennas and electronics which have a perfectly clear line of sight to the valley below. Clandestinely placing a sensor package here that is able to collect certain emissions while blending in with the clutter seems like a relatively rudimentary task‐hiding in plain sight if you will.
This is just one area of a fairly large complex of observatories and other buildings, many of which are in disuse, but which may already be adorned with antennas and other electronics and have an unobstructed line-of-sight towards White Sands. Otero County Sheriff House's comment in which he states there were officials and workmen inspecting towers and antennas could indicate that there were looking for just such a device.