Okay. It's taken me some effort, but I've figured out what you need to look for.
Palette data is written to palette RAM using the registers FF68, FF69, FF6A and FF6B. Registers are special memory values that allow the game software to access certain hardware functions - controller input, for instance.
In this case, we're primarily interested in FF69, which writes data to the BG palette RAM. Run the game in BGB, wait until just before the game loads the menu palette, and then use "access breakpoints" under the Debug menu in the debugger to set a write breakpoint for FF69 (type FF69 in the "addr range" field, make sure "on write" is checked and "on read" is unchecked, and click "Add"). This should catch the game in the act of writing the menu palette to palette RAM. Now we can find out where the palette data is coming from: hopefully, it'll be somewhere in the ROM (addresses 0000-7FFF), but if not, look at the RAM address indicated and see if you can find it there. We can then repeat the process, only this time, we'll set a write breakpoint for the RAM location of the palette in order to find out where it's coming from.