Is there a way to count pulses (a steady 120hz) for a changing length of a butt

Is there a way to count pulses (a steady 120hz) for a changing length of a button.

Im trying to count pulses that are a steady 120hz, for a length of time, that time is variable upon the amount of time that passes between each button push. pulsin wont work because its max pulse width is too small.

so basically I want to

COUNT pin, (duration is time between button presses), variable

Is it possible for me to count a signal AND monitor a button press for a desired state?
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