diff --git a/news/13793.bugfix.rst b/news/13793.bugfix.rst
new file mode 100644
index 00000000000..516ba51d446
--- /dev/null
+++ b/news/13793.bugfix.rst
@@ -0,0 +1 @@
+Include the underlying exception type/message in the self version check warning to improve diagnosability.
diff --git a/src/pip/_internal/cli/index_command.py b/src/pip/_internal/cli/index_command.py
index 0f1ee1a4f82..ba9491907e1 100644
--- a/src/pip/_internal/cli/index_command.py
+++ b/src/pip/_internal/cli/index_command.py
@@ -190,6 +190,10 @@ def handle_pip_version_check(self, options: Values) -> None:
             )
             with session:
                 _pip_self_version_check(session, options)
-        except Exception:
-            logger.warning("There was an error checking the latest version of pip.")
+        except Exception as e:
+            logger.warning(
+                "There was an error checking the latest version of pip. (%s: %s)",
+                e.__class__.__name__,
+                e,
+            )
             logger.debug("See below for error", exc_info=True)
diff --git a/src/pip/_internal/configuration.py b/src/pip/_internal/configuration.py
index e164653bbc2..0816de012cc 100644
--- a/src/pip/_internal/configuration.py
+++ b/src/pip/_internal/configuration.py
@@ -378,9 +378,16 @@ def _get_parser_to_modify(self) -> tuple[str, RawConfigParser]:
         assert self.load_only
         parsers = self._parsers[self.load_only]
         if not parsers:
-            # This should not happen if everything works correctly.
+            env_config_file = os.environ.get("PIP_CONFIG_FILE")
+            if env_config_file and not os.path.isfile(env_config_file):
+                raise ConfigurationError(
+                    "Cannot modify pip configuration: "
+                    "PIP_CONFIG_FILE is not a regular file: "
+                    f"{env_config_file}"
+                )
+
             raise ConfigurationError(
-                "Fatal Internal error [id=2]. Please report as a bug."
+                "Cannot modify pip configuration: no configuration file is available."
             )
 
         # Use the highest priority parser.
diff --git a/tests/functional/test_configuration.py b/tests/functional/test_configuration.py
index b235212477a..3c8b8c6670e 100644
--- a/tests/functional/test_configuration.py
+++ b/tests/functional/test_configuration.py
@@ -216,6 +216,22 @@ def test_config_separated(
             result.stdout,
         )
 
+    def test_config_set_with_pip_config_file_devnull_shows_human_error(
+        self, script: PipTestEnvironment
+    ) -> None:
+        script.environ["PIP_CONFIG_FILE"] = os.devnull
+
+        result = script.pip(
+            "config",
+            "set",
+            "global.index-url",
+            "https://example.com/",
+            expect_error=True,
+        )
+        assert "Fatal Internal error [id=2]" not in result.stderr
+        assert "PIP_CONFIG_FILE" in result.stderr
+        assert "not a regular file" in result.stderr
+
     @pytest.mark.network
     def test_editable_mode_default_config(
         self, script: PipTestEnvironment, data: TestData
diff --git a/tests/unit/test_commands.py b/tests/unit/test_commands.py
index 04ddd0316cc..915023ce22e 100644
--- a/tests/unit/test_commands.py
+++ b/tests/unit/test_commands.py
@@ -1,3 +1,4 @@
+import logging
 import os
 from typing import Callable
 from unittest import mock
@@ -158,3 +159,27 @@ def test_list_pip_version_check(version_check_mock: mock.Mock, flag: str) -> Non
         version_check_mock.assert_called_once()
     else:
         version_check_mock.assert_not_called()
+
+
+@mock.patch("pip._internal.cli.index_command._pip_self_version_check")
+def test_handle_pip_version_check_warning_includes_reason(
+    mock_version_check: mock.Mock, caplog: pytest.LogCaptureFixture
+) -> None:
+    mock_version_check.side_effect = PermissionError("Access is denied")
+
+    cmd = create_command("install")
+    options = cmd.parser.get_default_values()
+    options.disable_pip_version_check = False
+    options.no_index = False
+
+    with mock.patch.object(
+        cmd,
+        "_build_session",
+        side_effect=PermissionError("Access is denied"),
+    ):
+        with caplog.at_level(logging.WARNING):
+            cmd.handle_pip_version_check(options)
+
+    assert "There was an error checking the latest version of pip." in caplog.text
+    assert "PermissionError" in caplog.text
+    assert "Access is denied" in caplog.text