Is there a brightness switch for the AOA gauge on the F-16?
The F-16's manual is declassified since it's in service in many countries.
AOA Indexer
The answer is yes, the switch (lever) is conveniently located on the gauge. From said manual:

AOA Indexer
(...)
A dimming lever, located on the left side of the indexer, controls the intensity of the lighted symbols.

And here's a photo from airliners.net (red arrow):



AOA Indicator
In case you mean the AOA indicator on the instrument panel (yellow arrow above), then no, it doesn't have its own separate lighting. It will be the instrument panel light switches aft of the flight stick.


Source: airman.dodlive.mil; click here for the switches schematic (first two rows)