How can I persist GH_TOKEN for Github CLI with Codex?

I am trying to use Codex to (1) create issues on Github and (2) submit PRs to resolve issues. However, to access Github CLI, I need the secret GH_TOKEN to persist, even after environment setup.

I have tried using GH_TOKEN as an environment variable instead however, that will trigger a manual verification process (redirecting you to a webpage).

Codex (Cloud) Secret Injection (1263867) only resolves one time authentication (is not persistent).

Codex best practices for persistent secrets (1286607) offers no solution and does not specifically consider Github CLI usage.