Normally closed semiconductor switch
Switching with an active control signal turning the AC switch ON is easy.

Best bet is to AC-couple the signal and use that 20 mA to bias a PIN diode as an RF switch.  At 10 MHz, just about any small-signal diode will do.







simulate this circuit &ndash; Schematic created using CircuitLab
A relay also might work.   The 20 mA current will be a bit low for off-the-shelf items, however 3V, 500 mA reed relay

Oddball solutions include using a heater to bend a bimetallic member
and operate a thermal switch.   There's unlikely to be an off-the-shelf
unit that will be suitable.