Thank you!!! (and Thanks to whomever sent you that suggestion, too!)
I have a modulator with which I have to do exactly that, in order to get it to switch from the Dish receiver (connected via red/white/yellow composite cables) to whatever I have connected to the modulator's coaxial input, due to the Dish receiver always outputting a signal on those cables, even while in standby. (The modulator is supposed to switch automatically to the composite input when there is a signal, and then switch back to coaxial when that device is turned off.)
Rather than unplug the modulator all of the time, I simplified this by plugging it into a switched plug unit that is controlled by a remote control. Now, I can just press a button on that outlet's remote to switch back-and-forth. It sounds like the same solution may work for switching between Hopper+ and Hopper 3. The only difference is that the modulator switches instantly, while the Hopper 3 requires a 20-minute wait afterward.