This is a circuit that builds on KR5L’s zero-beat indicator circuit. He suggested trying a CMOS version of the 567 instead of the standard bipolar version, and here it is: the QRP version of his circuit. It draws only 0.9 mA at 5V compared to about 20 mA/8V for the original circuit.
Compared to the original circuit, C2 and C3 have been divided by about eight, and C1 has been divided by about two, give or take values found in my junk box.