When studying for one of the ham exams a few years ago, I learned that a radio can be detected and located even when not transmitting, just receiving.
In order to select a particular frequency (receiving or transmitting) a portion of the circuit, a Local Oscillator (LO) is necessary. It is a trivial trigonometry problem to locate a radio signal by Direction Finding (DF). "Foxhunting" is a type of ham radio contest using signal strength DF to find a particular radio.
Newer radios, like my ICOM IC-7300, use software processing for functions previously served by hardware, hence "Software Defined Radio" (SDR), but even SDRs have an LO circuit. In my radio the LO is part of a Field-Programmable Gate Array (FPGA) chip. Other radios use different solutions, but as far as I know, all radios have a locatable LO.
The block diagrams are specific to my 7300, but illustrate the point: Even when not transmitting your radio can be located.
