ok, so they cannot do ground training at all using a flight training device or sim? Not talking about flying with the students in the air, just ground training for IR and proficiency training. I ask, because the regs do not specifically say, but people in other forums and Wikipedia mention that they can train in a sim or FTD.
Your original question regards whether the holder of a ground instructor certificate with an instrument ground instructor rating on it can conduct ground training in a simulator or flight training device.
The answer, given and quoted in the regulation above, is YES; the ground instructor can do that. The IGI can provide ground instruction for the instrument rating, or for the instrument proficiency check.