GitHub connector might fail the connection test with the below error despite the PAT (Personal Access Token) used in the connector would have full permission in the account.
This can happen when the Github organization has SSO enabled and enforced so that all organization members must authenticate via an identity provider.
In order for a PAT to be able to connect to the SSO enforced organization, you must first authorize the token. Please refer the doc to authorize a PAT to be able to connect to a SSO enforced organization