Make sure you have the email address and password associated with the apple ID that works the imessages and facetime account to hand, this will usually be the same email login and password as your appleID / appstore account on ios etc.

click the go menu from the finder and select > utlities > when the utilities window opens up, double click the ‘Keychain Access’ application to launch it.

in the ‘keychain access’ window search slot – search for anything with facetime in the title and delete those specific items

in the ‘keychain access’ window search slot – search for anything with imessages in the title and delete those specific items

ie with them selected hit the delete key or right click and select delete, dont worry if they don’t appear to disappear, they will once you refresh the search in the search slot(a little keychain access bug there)

what we deleted are mainly digital signing signatures security certs / password and encryption keys related tat for the two pieces of software in question and can be easily recreated by the software again when logging in, once the facetime and imessages items have been deleted from keychain access.

within imessages and facetime application preferences sign out if your logged in still in either program and then log back in once more to facetime and imessages apps with your original login you have tested elsewhere and know to be correct, and all should now be good.