When batteries run low on charge, they sag under load, any kind of load. Your DMM does not load the battery and as a result, you might get the impression that the battery is in good condition when it's not. If you want to test a battery, it needs to be loaded to get an accurate result. At the very least, measure it while it's connected to a pedal and the pedal is engaged.
When you run sound thru a pedal, the battery current will likely change. Depends on the circuit. Opamps tend to draw a pretty steady current in most circuits. Discrete transistor designs like the Sunflower have variable current demand, depending on the bias and fuzz settings, playing style, etc. This caused the battery voltage to sag a variable amount while you were playing.
The LED is powered by the battery and when the battery voltage sags, the LED current goes down and consequently, the brightness goes down too.
Some people prefer the "dying battery" sound in certain pedals. The Fuzz Factory's STAB control can simulate an extreme case of battery sag.
FYI, in a lot of pedals the LED draws more current that everything else in the pedal. To help preserve battery life, disengage the pedal when you Take 5.