Replace CustomButton with the name of the specific button if it's different. RGB numbers indicate red, green, and blue on a scale from 0 to 1. The first RGB sets the off color; the second sets the on color. (This code will set off to black and on to white).
Create a script in ToggleWoodwinds named Sync(), set its execution to Manual, and paste this code into it:
if (TogglePiccolo.x || ToggleFlute.x || ToggleClarinet.x) x = 1;
else x = 0;
Then in each of the other buttons, create a script named OnX(), set its execution to On Expression x, and paste this into it:
Now every time the state of one of the buttons changes, ToggleWoodwinds will check all of the buttons and update itself.
The Sync() script can be expanded by adding whatever other buttons you want to check into the if statement after a || symbol. The || symbol means or; the if statement is checking whether any of the buttons' x values are non-zero.