Chosen Solution

How do I unlink an old Google account from my phone

No, DO NOT reset the phone to factory settings yet or you may have the added hassle of needing to enter your Google account details that were previously linked from the device. First of all, make sure to enable developer options by tapping on build number 7 times which is located in Settings, About Phone, Software Info. Then enable OEM unlock in developer options before factory resetting the phone via settings or recovery menu. Also you can just remove the google account via the accounts section of the settings, the remove account is under the 3 vertical dot menu button on the top right when you select the google account under syncing.