I see the same thing on iPhone XS and I posted about it on this forum (see here). The culprit in my case is the weather app on my Apple Watch. If I change the setting of weather to never, or turn off Apple Watch, the location service icon disappeared. I'm not alone as other users also posted about this on Reddit.
Thank you! Glad I'm not the only one who's encountering this. Took the weather app off my Apple Watch and sure enough the hollow arrow is now gone. Hope this will be fixed on the next release. I do like the weather app on my watch.
This issue seems to be resolved in iOS 13.1.
This is how it looks for me, no battery drain I can see but just annoying.
Interesting. It seems to solve the constant on icon issue for me. I have a Watch Series 3. I use the modular watch face with weather in the middle. Here is what my home screen on iPhone looks like about 10 seconds after opening the weather app on watch and closing it.
View attachment 863230
Settings>Privacy>Location Services and look at all the solid purple arrow to see which apps and System Services have use location recently.
About privacy and Location Services in iOS, iPadOS, and watchOS - Apple Support
Learn how privacy settings and Location Services help protect your personal information on your iPhone, iPad, and Apple Watch.support.apple.com