SS1.0, unfortunately :3 I figured out a way but not sure if it's the most efficient. I was able to add a URL parameter in the external code that defines which method was used. I then use request.getParameter('func') to get that value.

You can use GET/POST method as well

If I understand correctly, that shows only whether it's a GET or POST method, right?

Yes but you can use different method to access the two function.

I'm not sure what you mean 😞

BEst would be while calling add an extra header like SuiteScript - Call A and SuiteScript - Call B. Or even the URL param should work. What @samyt mentioned is good if A is a Get and B is Post call