Some Chevy and GMC trucks have power to their 7-pin trailer connection all the time, while other require the vehicle to be running. My Ford only supplies power when the truck is running.
Many trucks are missing a relay and fuse (found under the hood). You'll have to investigate your truck for the answer.
Check pin 1 to pin 4 on your truck's 7-pin connection with a volt meter or 12V test light.
2015 Wildcat 282 RKX
2011 F350 Lariat, 6.7 L. Diesel, 8 ft., SRW, Reese R20