RE: eConnect 2013 with Window Server 2016 or 2019
As Richard mentioned, if Dynamics GP will work with the operating system version, then eConnect will probably work as well.
That being said, the 'supported' environment would be to have Dynamics GP and its associated applications, i.e. Integration Manager, Web Services, eConnect, etc., all on one of the operating systems that is mentioned for that version of Dynamics GP in the System Requirement pages.
With Dynamics GP 2013, the 'supported' operating systems range from Windows Server 2008 through Windows Server 2012:
docs.microsoft.com/.../mdgp2013_system_requirements
I just mention this as, while it may work, should you come to support for an issue with eConnect, you may be asked to go to a supported OS environment for troubleshooting.
Thanks