Are you referring to the “Meter Control Button” on the lower left side (as you face it) of the lens mount?

See page 40 here.

http://www.cameramanuals.org/nikon_pdf/nikon_fa-1.pdf

Note: with the “Shooting Mode Selector” set to “Manual” the meter is in center-weighted mode regardless of the position of the Meter Control Button.

The second part of the manual is here

http://www.cameramanuals.org/nikon_pdf/nikon_fa-1.pdf

The manual ought to answer most of your questions regarding the use of the FA.

I've no idea why the MCB would be missing. Tampering by a previous owner sounds possible.

In normal operation you'd push in the MCB to override “Automatic Multi-Pattern Metering.” That sets the metering to center-weighted in any of the auto exposure modes: Program, Aperture Priority, Shutter Priority. Otherwise the auto modes use AMP metering.