Answer
Reinstall the Print Agent's Windows service, making sure to specify the service account with its domain prefix explicitly (DOMAIN\USERNAME), not just the bare username — omitting the domain is a common cause of this failure. The full sequence: uninstall the existing service from Print Agent, confirm it's actually gone via Windows Services, exit and restart Print Agent, confirm the REST port is correctly specified and open on the machine, then reinstall the service with the correctly domain-qualified account and start it again.