How fast is "really fast"?

A normal car (computer, fuel injection, O2 sensors), doesn't keep
the air/fuel ratio the same all the time. It's actually going rich, lean,
rich, lean, rich, lean all the time, maybe up to 10 times per second.

It does this for a few reasons, the main one being to check the O2 sensors.

The computer makes the engine run rich, and expects the O2 sensors
to indicate "rich", within a certain time, and to the level it instructed.
It then goes lean, and expects the O2 sensors to follow with a "lean" signal.
If the sensors don't follow fast enough, or far enough, the computer assumes
there's a problem, sets an error code, and turns on the Check Engine light.

Those gauges are actually designed for carbureted cars, so you can tune it
up without sticking your face behind the tailpipe to see if it smells like gas.

I assume it uses a narrow band oxygen sensor, as most such gauges
do. They  really aren't designed to be used like this. They only
reliably indicate rich or lean.

You need a wideband analyzer if you want reliable data.

Thomas

I have an A/F ratio gauge and it appears you don't know what it does.  Why
did you install it in the first place?  If you RTFM, maybe you'd understand
why it's doing what it's doing.