try this

README.md

@@ -55,8 +55,8 @@ are welcome! ❤️
 
 - **`github-token`:** GitHub token to use for authentication when pulling and
   pushing to the GitHub instance defined by `github-server-url`. By default this
-  uses `github.token`. Change this to a personal access token if you intend to
-  do things that go beyond the scope of the current repository.
+  is unset. You can set this to `github.token` or a personal access token if you
+  want to configure GitHub authentication globally.
 
 - **`github-server-url`:** Server URL like `https://github.example.org` to use
   as the scope for the `github-token`. By default this uses `github.server_url`

action.yml

@@ -9,10 +9,9 @@ inputs:
   github-token:
     description: >
       GitHub token to use for authentication when pulling and pushing to the
-      GitHub instance defined by 'github-server-url'. By default this uses
-      'github.token'. Change this to a personal access token if you intend to do
-      things that go beyond the scope of the current repository.
-    default: ${{ github.token }}
+      GitHub instance defined by 'github-server-url'. By default this is unset.
+      You can set this to 'github.token' or a personal access token if you want
+      to configure GitHub authentication globally.
   github-server-url:
     description: >
       Server URL like 'https://github.example.org' to use as the scope for the

src/main.ts

@@ -60,7 +60,7 @@ if (userName && userEmail) {
   await $({ stdio: "inherit" })`git config --global user.email ${userEmail}`;
 }
 
-if (githubToken && githubServerURL) {
+if (githubToken) {
   const prefix = new URL(githubServerURL).origin + "/";
   const basicAuth = Buffer.from(
     `x-access-token:${githubToken}`,