Thank you for your help Nurahmadi. I will look for gitlab forum solutions.

If I move the following location section inside the gitlab-http.conf file both GitLab and Jenkins proxy_pass will works

Assuming that modifying the omnibus version of gitlab-http.conf is the only way to make it work, then my problem has changed
to how do I maintain gitlab-http.conf?

My problem is that all modifications will be destroyed if I ever run gitlab-ctl reconfigure.

Hopefully I can find a gitlab user forum to research solutions to maintaining custom code in
gitlab-http.conf

location ^~ /jenkins {
proxy_pass http://localhost:8081;
proxy_read_timeout 90;

# Fix the “It appears that your reverse proxy set up is broken" error.
proxy_redirect http://localhost:8080 $scheme://example.com;

# Optionally, require HTTP basic auth.
# auth_basic "Please authenticate to use Jenkins";
# auth_basic_user_file /opt/nginx/htpasswd;
}