The Assign Switches are often used to change output level in a Part, but can also be used to change Effects or literally a score of other things.
If you wish to ask a question about what the assignable button is set to do, let us know specifically what Performance, we'd be happy to help you explore.

Latin Flutist. The Asgn 1 removes the vibrato but Asgn 2 is half lit and does not light up when touched. The "all" displays the controllers but there's no assign 2 listed. Not sure why it's lit if it has no function.

I think I read that "half lit" means illuminated so that you can find the button but not currently in use.

I thought that "half-lit" means that it has an assigned function. If not lit then it does not. Under the controller common for part 1, the diagram clearly shows that the leader line goes to the assign #2 switch. Under "performance control" it appears active but there's nothing assigned to it below but it says "Display Filter" in the box. Not sure what that means but when you select it nothing appears to happen.

The Contra Bassoon even has the SW2 control number turned off and the button is still lit. This button also appears to do nothing but is half-lit. When I added a valve then it would become brighter when pressed but the sound was cut-off.

PS: If you happen to lose volume like I just did again, just tap the performance again and it should come back up to a normal level.

Controller Number assignments are customizable on a per Performance basis. The Assignable Switch 2 is not assigned a control number in the "Latin Flautist, normally it is set to cc87. The AssignSw2 is set to "Off" (no cc number). Not sure what they originally had in mind... But I can make an educated guess... by setting the Switch's assignment to Off, they prevent the flute from being removed... You can analyze the Performance as follows:
PART 1 = Flute 7 Elements
PART 2 = Acoustic Guitar 4 Elements
PART 3 = Vibraphone 2 Elements

Part 1, Element 1is set XA CONTROL = AsgnSw1 On, which means in all other conditions of the Switches it will not sound. This AsgnSw1 switches to a Flute Waveform without vibrato. The other six flute Elements construct both the vibrato flute (velocity switching) and the legato flute (velocity switching). There is a staccato Waveform triggered on quick attacks. There is also an 'Easter egg' (hidden surprise) where if you play "legato" and exceed a velocity of 110 thru 127 you get the flutter tongue articulation.

I'm going to guess they used a flute that actually had the Assign Sw2 set to control something but replaced it with the guitar and vibes, and rather than rebuild that component simply opted to set the As Sw2 controller Off. I think they wanted to provide a method to play the flute, sans vibrato, and with that staccato chiff, on demand.

Hope that helps