Been doing EVP sessions near some of the older burial grounds out on Dartmoor for about three years now and yeah, consistently picking up something. Not white noise pareidolia either - proper structured vocalisations that weren't there when I was recording.
The one that still gets me was a session near a Bronze Age site, nothing overtly "cemetery" about it but the ground has human remains going back thousands of years. Got what sounds like a male voice, two syllables, right in the middle of about forty seconds of clean ambient sound. No wind disturbance, no one else around, I'd checked the area beforehand.
What recorder are you using? I've found the results vary massively depending on the kit. My old Olympus picks up things my phone mic completely misses, not sure if its the frequency range or what.
Would be interested to know if anyone's noticed a difference between genuinely old burial sites versus, say, Victorian churchyards. My experience suggests the older the site the more activity but that's purely anecdotal at this point.