Asking for hint: annunciators and HGR

I am not sure what you are referencing but starting with the Apple IIe that has "double width" graphics there are I/O locations that affect graphics. These graphics soft switch locations overlap with the annunciator lines in the joystick DIP socket.

https://www.kreativekorp.com/miscpages/a2info/iomemory.shtml

C058 49240 CLRAN0       OE G WR   If IOUDIS off: Annunciator 0 Off
           DISXY          C  WR   If IOUDIS on: Mask X0/Y0 Move Interrupts
C059 49241 SETAN0       OE G WR   If IOUDIS off: Annunciator 0 On
           ENBXY          C  WR   If IOUDIS on: Allow X0/Y0 Move Interrupts
C05A 49242 CLRAN1       OE G WR   If IOUDIS off: Annunciator 1 Off
           DISVBL         C  WR   If IOUDIS on: Disable VBL Interrupts
C05B 49243 SETAN1       OE G WR   If IOUDIS off: Annunciator 1 On
           ENVBL          C  WR   If IOUDIS on: Enable VBL Interrupts
C05C 49244 CLRAN2       OE G WR   If IOUDIS off: Annunciator 2 Off
           X0EDGE         C  WR   If IOUDIS on: Interrupt on X0 Rising
C05D 49245 SETAN2       OE G WR   If IOUDIS off: Annunciator 2 On
           X0EDGE         C  WR   If IOUDIS on: Interrupt on X0 Falling
C05E 49246 CLRAN3       OE G WR   If IOUDIS off: Annunciator 3 Off
           Y0EDGE         C  WR   If IOUDIS on: Interrupt on Y0 Rising
           DHIRESON      ECG WR   In 80-Column Mode: Double Width Graphics
C05F 49247 SETAN3       OE G WR   If IOUDIS off: Annunciator 3 On
           Y0EDGE         C  WR   If IOUDIS on: Interrupt on Y0 Falling
           DHIRESOFF     ECG WR   In 80-Column Mode: Single Width Graphics

If you refer to Jim Sather's Understanding the Apple IIe, it explains the function of the AN3 soft switch ($C05E) to insert a delay into the video encoder, which changes the color palette by altering the phase relationship between the bitstream and the colorburst.