I have noticed lately that the GPS icon comes on and off on my phone even with the GPS off. I'm afraid the phone is using more battery by doing this.
The GPS receiver itself uses barely more power than the battery uses when sitting on a shelf. Switching the LCD display on and off probably uses more (and that's almost zero).
There is a problem with the phone - a display problem - but even leavng the GPS receiver on full-time isn't going to drain much battery.
I saw this earlier and tried this. Go to settings>privacy and safety>location>google location history>turn it off. Even though my location is off it kept pinging it. since I turned google location history off its stopped.