For the life of me I've never seen technical documentation on the way Gamecube generates composite or s-video. (RGB in PAL) Let alone NTSC/PAL color mod attempts no matter how futile. Though one very old article suggests the interesting possibility of modding between s-video/RGB, pipe dream as that sounds. http://www.eurogamer.net/articles/a_cubeeuro
Amazingly author of that eurogamer article still working there. Though in that article maybe he is talking about component cable modification. You need to lift pin on DAC inside and solder a resistor. Wii output can be modded by converting to PAL console afaik. So maybe GC output mode configured through BIOS initialization routines.
What about de-soldering the internal DACs from an NTSC and PAL motherboard, to swap them? I don't know if there's PCB or other differences to stop that.
The Gamecube digitally synthesizes composite and S-video, both NTSC and PAL, from its standard CCIR-601 27 MHz seed clock. NTSC and PAL consoles probably have identical (integrated) DACs, though quite clearly different output amplifier topologies and wiring. The encoder however could be fixed in hardware such that "color mods" are next to impossible, or stuff could be software controlled and require individual game patches or a loader.
Yeah I wouldn't count on serious experiments anytime soon. Pretty sure much of the practical benefit is made obsolete by Wii controlling it in software, though I haven't tried to region change a Wii.
Also unless you're limited to a RGB monitor or old SCART TV, there isn't a point in choosing RGB over YPbPr component with a modern console anyway. In most cases they literally have identical video quality (the exception would be if uncompressed 4:4:4 YCbCr isn't available, yet 4:4:4 RGB is), and the color accuracy is a toss-up since internally RGB and YCbCr are getting converted back and forth digitally leading to small rounding errors all the time. In the case of the GC I believe YPbPr to actually be more accurate than RGB since the digital video output is strictly lossy 4:2:2 YCbCr. When people mod the component cable to output RGB, they're getting the same lossy YCbCr, simply transcoded to RGB... Very pointless, unless you have no other options. IMO people should leave the cables alone and just get YPbPr -> RGB transcoders.