Did some moderately quick and dirty testing, interesting results. Normal overmap range on fields seems to be 5 overmap tiles. Not really much further than the player can see really but eh. Equipping binoculars, having the scout mutation or having the telescopic eyes bionic increases that range to 10 overmap tiles, which is a pretty impressive bonus for how little it costs. The scout mutation and telescopic eyes or binoculars increases the range to 12 tiles, but binoculars and telescopic eyes seems to have no effect, which makes sense.
Perception doesn’t seem to have any effect, since the default range is 5 tiles with 5 perception or 50.