Thanks for the replies. After downloading Carrot, it seemed the GPS icon stayed on constantly. I will try it again and restart the phone too for good measure. (DarkStar only used the GPS when needed, but opened SO SLOW on the watch that I got tired of waiting)
Yep, I use a special feature on iOS called “significant location change monitoring”. Rather than keeping the GPS on all the time, it just updates when you’ve moved a significant distance from your last monitored location. This shouldn’t affect your battery in any way because it doesn't even use the GPS antenna, but Apple does keep the location arrow in your status bar so that you’re aware an app is using this feature.
It’s really useful for the Apple Watch because you don’t have to wait extra time for the GPS to wake up, triangulate your location, etc.
Of course, you can always turn off this feature if you like - just go to the Settings app, then Privacy, then Location Services, then find CARROT in the list and switch her from “always” to “while using”. Then she’ll only access your location when you open her.
And in case you're curious, I answered a bunch of questions on the CARROT Weather complication in this thread, by the way.