I want to do this:
the function I wish to connect to the others does use the requests library to hit both external and internal APIs but these links don't show in the application map.
Is there a way to connect them manually?
If the solution is not available using the portal, all code is written in python.
Simple answer: No, you cannot manually do anything in the Application Map, it's fully auto-generated.
The only thing you can try to do is better instrument your various components and apply proper distributed tracing in a way that AppInsights will pick it up and visualize it. But that can be a complex exercise, depending on your app (well worth it, though, if you ask me)