HI,
If you follow the link provided you will find that Joseph_S. meant for you to use a different Mac User account.
You can create a New Mac User account in System Preferences > Users and Groups.
Or your can Enable the Guest Account.
Your then Log out of your regular account and into the option you have chosen or created.
IF your Messages Login works here then the issue is in your Mac User Account.
If you happened to have Migrated that Mac User Account into the new OS then open Keychain Access (Applications/Utilities) and delete the IDS: yourAppleID-Auth Token from the Password pane of the Login Keychain.
If the Migration was from another computer then that Keychain Item holds a comnination of the ID, Password and the Mac Serial Number.
The login checks the Serial Number and if they don't match you can get logged out.
In the worse cases scenario you get Blocked at the iMessages Server based on the device using that ID.
This Block is Related only to the Apple ID when used from that Mac for iMessages.
Other apps such as iTunes can still use the ID as can the iCloud Login.
There is only one fix:-
When the iMessages account will not Login
The Phoning Apple can be long winded. It will be an Apple ID issue which is free to fix.
8:31 pm Tuesday; October 23, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
MacBookPro 15" 2016 (High Sierra 10.13.x)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)
