Hi.
The intention is to use a NE567 that will turn a LED on when frequency is 60Hz +/- 5Hz and two more leds for frequency being lower and higher.
Does the NE567 has any pin useable to tell if input is under or over the center frequency ?

It is for a adjusting the engine governors in portable generators, to be built in a wall wart case.

 

I only see a, "yes" output, not a high or low indicator. I'm sure you can use a phase locked loop to give you an error signal, high or low, but not this one.

 

The simplest in terms of parts count and most accurate solution will be a micro-controller. Only 3 LEDs and an optional quartz crystal needed. Count the clocks between zero crossings of the input. Compare to proper period.