How to setup a GTM virtual server with http and https backend services.

I'm assuming you have already added the BIG-IP system that has GTM and LTM on it as a GSLB server with Virtual Server discovery disabled. When you add a virtual server to that server's configuration, you should be able to specify any service port - 80, 443, etc. - in the Translation Service Port setting. And, yes, you must specify the full name (partition/path/object-name) of the virtual server, as configured in LTM. For example: /Common/http_vs

What version of GTM are you running, by the way?