HAP Lands with a Private Tag?

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If someone has a turkey tag for private lands (ZZ and 234 in the ZZ unit), can they use this tag on HAP lands?

I ask because through the research I've done, I can't find anything stating one way or another. The closest I've found that somewhat relates is if I shot a doe on HAP land, I would have to tag it with my private land doe tag.

HAP Lands with a Private Tag?