Woohoo! I found a Sega brand manual RF switch (model number SS-60) at my local used electronics shop (Hard-Off) for 500yen. Looks the same as an old Atari or TI-94/A RF switch, so thanks a lot guys! Works like a charm on the SG-1000. Doesn't work on the Mark III for some reason. Maybe the RF connection in the Mark III is dead? Oh well, it has AV so I'm happy.
Still hunting for some controllers for the Mark III. MSX controllers definitely don't work, as I tried that yesterday. :P