I actually did not have dim on brake light condition. Mine presented differently. (BUT, I did notice that just holding down the brake pedal would cause the voltage to creep upward continuously for as long as I held it (beyond normal driving, like 5 minutes). (I don't know how high it would creep if held indefinitely.)
(With LED in ashtray bulb) - RED/BLK voltages:
Key at position I: ~0.3V
Turn key to position II: ~2V (Interior doesn't dim, not quite enough voltage)
(Key at II) Turn on parking lights: ~12+V
(Key at II) Turn off parking lights: ~3V (interior STAYS DIM, additional 0.8-1V remains in the circuit)
Turn Key to III, release back to II: ~2V (cutting power to most things to start the car would "reset" voltage)
Turning Key from II back to I: ~0.3V
With stock bulb in ashtray, voltages in RED/BLK when headlight switch is off was well under 1V at all key positions.
Stuff I messed with (with ashtray bulb as LED):
Removing Fuse 5 would keep RED/BLK at 2V on headlight switch cycle, displays were normal behavior at all times.
Removing Fuse 4 or unplugging the 30P connector on the Climate Control Unit would reduce RED/BLK voltage to less than 1V at all key positions. Swapping CCUs did not change anything, (even with a brand new one). Displays normal at all times. Unplugging 14P CCU connector doesn't do anything.
Key at II - Unplugging the Dash Lights Brightness Control Unit (behind TCS ECU) would raise the voltage to 3.1V instantly, regardless of headlight switch (could stay off, never cycled). Reconnecting it would reduce voltage to 2V, displays reset to bright. Swapping DLBCU to new unit didnt change anything. Using jumper wires, only RED/BLK connection would change voltage (3V -> 2V), other 4 wires don't affect anything.
Key at II, RED/BLK at 3V from headlight cycle - Unplugging RH cluster connector, then reconnecting it, would drop voltage to 2V, displays reset to bright.
Removing Integrated Control Unit (38600-SL0-A01/A02) did not affect voltages much. Did not affect display behavior, issue remained. I bought a new one, but got the wrong part (-G01), and putting that in gave me a brake lamp warning on the dash. Not sure why, but that was curious.
Unplugging the headlight switch itself (LH steering stalk controls) after cycling didn't change anything. Swapping to a used unit didnt change anything.
Unplugging RH steering stalk controls didnt change anything.
Unplugging the turn signal cancel unit after cycling headlight switch didnt change anything. Changing to new unit didnt change anything. Headlight switch grounds through this (purple wire), so it must be connected to activate parking/headlights.
Unplugging popup headlight/brightness control (near LH cluster) didnt change anything.
Unplugging LH door switches didnt change anything.
Removing Fuse 34 didnt change anything.
Unplugging my LED tail/brake assemblies didnt change anything. Nor did side markers, nor did parking lights. RED/WHITE on fuse 39 was exactly the same as RED/BLK on fuse 38.
Not sure any of that helps, but just things I discovered on the long journey.