Can you get into diagnostic mode? Service manual has this to say if the illumination day/night mode isn't working properly:
Go into the System Diagnostic Mode, and use the Car Status test (see page 23-192) to check for an ILL signal.
Is the ILL signal OK?
YES-Replace the audio-navigation unit (see page 23-232).B
NO-Check the ILLUMI+ circuit between the audio-navigation unit and the No. B29 (10 A) fuse in the under-dash fuse/relay box.
To enter System Diagnostic Mode: hold the three buttons (MAP/GUIDE, MENU, and CANCEL), for about 3 seconds. The display screen goes directly to the Select Diagnosis Items menu shown.
Detail Information & Setting (allows you to manually diagnose the navigation system)
Touch Car Status
Use this screen to confirm that the audio-navigation unit is properly receiving input signals. Signals equal to (0) are OFF, and signals equal to (1) are ON. If the value on the display does not match the actual vehicle status, then check the wire carrying the signal.
VSP-Vehicle Speed Pulse from the ECM/PCM (audio-navigationunitconnectorA(24P)terminal No. 23)
a) OFF (0) when vehicle is not moving
b) ON (1) when vehicle is moving
The VSP comes from the ECM/PCM as a dedicated signal. Internally, the audio-navigation unit compares the actual VP on the map against street data to adjust the pulse to speed scaling factor. As this scaling factor becomes more accurate, the Level gradually increases from 0 to 10.
BACK-Reverse indication from taillight relay (audio-navigation unit connector C (8P) terminal No. 8) a) OFF (0) when the shift lever is in any position other than reverse
b) ON (1) when the shift lever is in reverse
The Back signal is used by the audio-navigation unit to allow the map screen to show the VP moving backwards when in reverse. This signal is needed because the Speed Pulse does not indicate direction.
ILL-lllumination Indication (audio-navigation unit connector A (24P) terminal No. 4)
a) OFF (0) when parking lights, or headlights are off b) ON (1) when parking lights, or headlights are on
The navigation uses the signal to determine whether to put the navigation screen into the Day or Night brightness mode (Setup screen 1).
This item detects whether the illumination cancel function is in use.
a) OFF (0) when the dashlights brightness control button is less than 90 % brightness with the headlights turned on.
b) ON (1) when the dashlights brightness control button is more than 90 % brightness with the headlights turned on.
I would use that screen to test what is happening with the illumination signal when you try all the variations posted in your video.