How should I probe when measuring output impedance? Why do I get inconsistent readings?
Cheap solderless breadboards have a lot of contact resistance. It can be 0.5 ohm to 1 ohm per connection. I am defining a connection as a wire or pin contacting the breadboard. I count 4 connections in your setup.
The contact resistance is not constant, but can vary based on the exact position of the inserted wire.
As a test, replace your resistor with a wire and measure the resistance between the top terminals in your picture. Short your meter leads and subtract this reading.