Hi PGAdams,
Logging out of an Apple ID for one user account would not effect any changes on the other. When signing out you may see a prompt to keep or delete the information for that user that's associated with the Apple ID but again, this should have no bearing on the second account. Sign in or out of your Apple ID on Mac details these steps further:
"Sign out of your Apple ID
Sign out of your Apple ID account to prevent others from accessing your account information and Apple services on your Mac—when you sell or give away your computer, for example. See the Apple Support article What to do before you sell, give away, or trade in your Mac.
- On your Mac, choose Apple menu > System Settings, then click [your name] at the top of the sidebar.
- Click Sign Out.
- Follow the onscreen instructions for copying and downloading your data stored in iCloud. For more information about signing out of your Apple ID, see If you sign out of your Apple ID settings."
Regards.