Originally Posted by Fabrik8

Sounds like you have a power or ground problem with the gauge, and the difference in voltage with engine RPM is making it brighter or dimmer. No idea. It should sweep from lean to rich more than once a second if it's working properly, except under fairly heavy throttle.

My advice on how to fix it:

Sell it.

You have a narrowband O2 sensor, and a narrowband gauge isn't really good for anything except entertainment. I won't bore you with the technical details of how the O2 sensor is read by the ECU, but take it on faith that the O2 sensor isn't very accurate. Any reading off of an inaccurate sensor is inherently an inaccurate reading. I'll explain why it sweeps back and forth from lean to rich like a metronome at part throttle if you want, it's boring but you may be interested.

If you want an actual idea of what your A/F ratio is, you'll need a wideband O2 sensor and gauge. Not cheap, but if you want meaningful data than that is what you get.