Yes, sounds like you want to sense the 3V signal, and use that to toggle a separately-powered flip-flop type circuit, which changes state on each interruption of signal. This could be done using a CMOS flip-flop, and would run for years even on a tiny battery. If you add an LED indicator, that becomes the pacing item for how big a battery you would need. Using a Flashing LED would reduce the power drain somewhat.
Question: what does the output of the flip-flop control besides the LED? Some sort of audio switching? How much power does that take?