Here's a series of photos showing how to fit a language switch to the PAL Mega Drive II, based on information provided by Mark Knibbs. The US Genesis II, though I haven't seen one, should be very similar. Note that there may be different revisions of the main board, i.e. your console could differ somewhat from the pictures below.
 

Top Side Of Board

Look for a 208-pin chip marked 315-5660; it's the largest chip on the board. Pin 107 of this chip determines the language setting. When the pin is at +5 volts, it's English; when 0 volts (Ground), it's Japanese. On a PAL (European) or US console, this pin is hard wired to the +5v supply, via a trace which connects (through a plated through-hole) to a +5v plane on the underside of the board. The objective of this mod is to disconnect the plated hole from the +5v supply by cutting around it, then soldering a wire to the hole which is in turn connected to the centre of a SPDT toggle switch. The other connections of this switch are linked to +5 volts and Ground, allowing the console to be switched between Japanese and English mode as desired.
 

Underside Of Board

Flip over the board and look for the hole we're going to cut around. It's indicated by an arrow in the picture below; the cut has already been made on this board.

Get your Stanley knife or craft knife and make four cuts in a diamond shape, to isolate the hole from the surrounding copper while being careful not to break the connection of the copper trace itself in any way. A multimeter or continuity tester will come in handy here: scrape off some of the green "solder resist" coating as shown, so you can make contact with your meter probes. Once you're absolutely sure the hole has been disconnected from the +5v line, flip the board back over.

Scrape away the solder resist from the top side of the hole, indicated by the arrow. Be careful not to damage the trace! Solder a wire to this point, then connect the other end of the wire to the centre of your switch. The Ground and +5 volt connections can be obtained from the right hand side of JP3 and JP4, respectively.