Building a Comparator
IF - what you want is for the start of an output pulse to enable the 2nd 555 to start clocking the counter, and the reception of a reflected pulse to inhibit the 2nd 555 ...
THEN - place a set-reset flipflop in front of the 2nd 555.  Set it with the output pulse, reset it with the received pulse, and its output goes to the 555 enable.
NOTE - Coming out of the reset state or power-on, the first half-cycle of a 555 astable circuit output is longer than all of the succeeding cycles and half cycles.  This is because for that first half-cycle only, the timing cap is being charged up from 0 V; in all following cycles it is being charged up from Vcc/3 V.