I don't have a lot of information to guide me, but I think you'll want to set the Upload Data part to Multipart/Form Data, since that's what their page contents state. If your data is stored in an attribute then you could use Specify Upload Body - I'm getting that information from this question: https://knowledge.safe.com/questions/28528/httpcaller-file-post.html - but I don't know if the web page you are writing to supports that.

I'm going to guess that each part of the form needs to be a separate line in the multi-part table in the HTTPCaller parameters. Alternatively construct it all in a single attribute, as this example suggests: https://knowledge.safe.com/articles/23297/boxcom-3-upload-a-file-to-a-directory.html

My other suggestion is to turn on Debug Logging (Tools > FME Options > Translation) as when you do this you get a lot more information in the log about exactly what the HTTPCaller is doing.

I hope this gets you going in the right direction. Apologies if not, I'm just trying to pull information from the extra sources at my disposal. If you're still having problems let us know and I can pass on the question to someone in our web/server team.