Unable to connect to Jenkins server in a subdirectory

Our Jenkins is accessed via a subdirectory, so effectively something like

http://ServerName:12345/Jenkins/

putting in this URL in the Jenkins Connection Settings results in:

• Response status code does not indicate success: 404 (Not Found).

using Fiddler, I was able to see that the subdirectory is being dropped from the request to the API endpoint. If I modify that request to include the subdirectory (request #3 in screenshot below), the response indicates success.