Using an iPhone as a cassette recorder for 80's home computer
The link in Michael Kohne's comment is the answer:


  The iDevice needs to see a resistance in the neighborhood of 5k
  between the microphone conductor and ground. That tells it that a
  microphone has been plugged in. If it is a direct short, it thinks a
  headphone was plugged in. Open circuit means nothing was plugged in.
  The exact value is not important, from experimenting I found that 4.7k
  seems to work. This resistor is put in series with the isolation
  transformer.


I found that by putting a 10k resistor across "computer tape in" and ground the iPhone switches to the external mic.  The record level is a fraction high - I don't know if that's related to the resistor or simply due to the signal from the Microbee.

Disclaimer: I have no idea what I'm doing, use at own risk!