In Av/Tv, the centered indicator does not mean the light is perfectly stable. It usually means the camera is automatically changing the exposure setting it controls to keep the metered exposure at its target, and the scale is effectively showing exposure compensation. If compensation is set to 0, the marker stays centered while shutter speed or aperture changes behind the scenes.

In Manual mode, the camera is no longer adjusting exposure for you, so the meter shows the actual difference between your current settings and what the meter thinks is the target exposure. As the scene or framing changes, that reading will move.

So Av/Tv is not inherently more "dependable" at finding average gray—it is just auto-correcting continuously. Manual gives you the live meter reading and leaves the correction to you by changing shutter speed, aperture, or ISO.

A centered meter in Manual is the same metered target the camera would try to reach in Av/Tv, based on the selected metering mode.