How to turn on a device with only 1 wire between itself and switch?
If you want to wrestle a little and not to go over, where the fence is lowest(=ready to use wireless system), you can try the following:



M1 and M2 are the magical units. You can probably connect capacitively because there surely is some big metallic parts - for example electric cables - that are quite near both magical units. P1 and P2 that make the connection are insulated metal plates or long enough insulated wires.

You need quite high frequency, at least 50 kHz. Also you must modulate something detectable to avoid false alarms. So, let M1 be a 50 kHz oscillator + a pulser that amplitude modulates the oscillator by 500 Hz. M2 is the following:


a resonant bandpass filter that is tuned to 50 kHz
an amplifier
a diode detector
a tone decoder for 500 Hz, can be also a bandpass filter + level detector
proper buffering for your indicator


Note: 1) The receiver must be on continuously 2) You must have quite pure transmitter signal to stay off from radio bands. An easy to make square wave transmitter can disturb AM radios at several hundred meters.