More Words, Deeper Hole

The title in the radio play, indeed, sounds like "The Mule Finds".

The chapter titles in the Second Foundation book are nothing like these though. The entire Mule section of the book Second Foundation consists of:
PART I - Search by the Mule
1. Two Men and the Mule
2. Two Men Without the Mule
3. Two Men and a Peasant
4. Two Men and the Elders
5. One Man and the Mule
6. One Man, the Mule—and Another

And from briefly listening to the beginning of the radio play, it does indeed start with the events from chapter 1.