I also came across a similar issue when using VS Code with remote containers and Docker Desktop (WSL2).

I debugged the problem by adding in a --pre-get-sources-script=ls -l "repo_directory", i.e. in the OP's case:

# docker run --name=runner --privileged -t --rm \
 -v /var/run/docker.sock:/var/run/docker.sock  \
 -v /tmp/.gitlab-runner/:/etc/gitlab-runner \
 -v {PWD} \
 --workdir $PWD \
 --pre-get-sources-script=ls -l /home/fox/Work/docker/core-application/../.git/modules/core-application \
 gitlab/gitlab-runner exec docker \
  --builds-dir /tmp/builds/ Rspec

In my case, the directory listing (ls -l ...) came up empty! I'm assuming that it mounts the directory as a volume within the container as the same name (/fubar:/fubar), which in my case isn't going to work as it is Docker Desktop with vscode remote containers.

My fix was was to add my named volume as a parameter to a secondary directory, and then setting the --clone-url to point to that directory.

Something like:

# pwd
/workspace/fubar
# gitlab-runner --debug exec docker \
  --docker-volumes vscode-workspace:/workspace2 \
  --clone-url=file:///workspace2/fubar \
  validate;
[output truncated]
...
Starting container 3d49d8e8b977177f34beeae3ae5f09eba288332e109ad79f133e0f160377908b ...  job=1 project=0
Fetching changes...
Initialized empty Git repository in /builds/project-0/.git/
Created fresh repository.
Checking out d1a39a4d as detached HEAD (ref is feature/FU-123)...

Skipping Git submodules setup
Executing build stage                               build_stage=restore_cache job=1 project=0
Skipping stage (nothing to do)                      build_stage=restore_cache job=1 project=0
Executing build stage                               build_stage=download_artifacts job=1 project=0
Skipping stage (nothing to do)                      build_stage=download_artifacts job=1 project=0
Executing build stage                               build_stage=step_script job=1 project=0
Executing "step_script" stage of the job script
...

I had originally tried changing the --pre-get-sources-script to be cp -R /workspace2/fubar /workspace/ but that complained that the target directory was read-only. Using the --clone-url=file:///workspace2/fubar worked, so I've left it that way.

since gitlab 17, the feature is removed https://docs.gitlab.com/runner/commands/#gitlab-runner-exec-removed