Pausing a clock signal generated by 555 timer
You can make the 555 oscillation stop without having to use any switch. Just connect your on/off signal to the RST input of the 555 chip. When the RST goes low the 555 will stop. When RST goes back high the 555 will resume generating the clock signal again.

If you want the circuit output to retain its last signal level when the clock becomes gated this is solved by running the 555 at twice the desired frequency. Then you use a D-Type FF to clock on the rising edge of the 555 output and connect it's D input to the QNOT Output. The FF will produce a nice 50% output duty cycle and will retain whatever state it was in when the 555 is forced into reset.