Now that I got an API Key I was able to test it.
I've tried it both with "Advanced REST Client" as well as directly with ThingWorx, in both cases I was not able to post the content as JSON to the request (as payload).
The only way that I got response was to compile the request completely into the URL:
Then I was able to get the response as JSON. That means for the Request Method it does not care if you are using GetJSON or PostJSON in ThingWorx (you are just using the URL parameter).
That means for a generic service you have to compile the URL string with appropriate input parameters.
Depending on the further usecase you may want to convert the JSON to an infotable afterwards.