I have a 1993 toyota pickup. My A/C turns on when I turn on the blower/fan not matter if it's on low or high, even if the ac bottom is not on the one with the green light. But it does turn off when I turn off the blower/fan

 

I'm not sure about your truck specifically, but most vehicles with A/C will automatically kick it on if you have the windshield defrost/defog turned on. switch your controls to foot or vent only and see if it shuts off.