[Dwedit]

GBA switching to GBC mode turns out to be combination of both hardware and software. There's a physical button that is read by the BIOS to see if it wants to perform a mode switch to GBC mode, then the BIOS triggers the mode change.

But that button is also responsible for making the cartridge bus actually function with GB/GBC cartridges. If you switch into GBC mode without the button being pressed, nothing can be read from the cartridge. (Normally the register bit that switches to GBC mode is locked out and only the BIOS can write it, but if you are executing code in the BIOS, a timed DMA transfer can perform that write.)