When I try to add my Github account on sourcetree using HTTPS and Basic authentication it throws me an Error saying - Failed to check login for user. Authentication required.
Did you try to log out and then log back into your GitHub account?
I know it sounds weird, but I had a somewhat similar problem (requesting authentication when I wanted to push changes) and that's what I did after seeing that GitHub recommended this kind of little handling.
(Potentially same kind of issue as Github Personal Access Token not working for Basic Auth)
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