Why did you add the ATtiny85 to the project while the ESP8266 is capable of doing all the work on his own ?
you can program the ESP8266 with the Arduino IDE. The sensor you use gives a digital signal. Much simpeler with the hardware
Voila, you answerd the question :)If the pulse outlet is an LED blinking for every X Watt, you just put a little photoresitor over a voltage devider on it going to the GPIO pin. Then write a program that handles the pulse. When ON, you 'arm' the counter, when OFF, you fire a sequence. Be aware of a kind of bouncing effect when the light turns off. The value will not allways be 0 straight away, but more ripple out. So build in a little delay in your program (20-50ms, anyway shorter than a pulse).
ESP8266 WiFi relay switch
ESP8266 webserver serving multiple pages
Kitchen Physics - Measure the speed of light with chocolate!
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