I'm having the same issue. i have an iphone 11 pro with most recent OS.
Actually had multiple conversations w/Apple Support over Twitter and a phone call w/support where they assigned a case #. Long story short - they say this is normal...I find it hard to believe as no other iphone i've owned has had this issue nor do the 4 other people in my house. Support told me they have a known issue where location services is shut off at the master level and the icon still appears. Supposedly engineering is working on a fix.
I actually stopped in a local apple store and spoke to a sales person. Upon hearing the issue, she looked perplexed at first than stated that "iphones, when they sense they are near other iphones ping each other looking for a connection".
I know 4 other people with iPhone 11 pro - we all set phone location settings exactly as mine and only 1 other person had this issue.
I have all apps set to "never" share location except find my iphone. Location arrow with show on home screen several times a minute. Even with locations services on, all apps at "never" and find my iphone off - arrow still appears.
Also, when you look at apps that may have requested location services, there are no gray or pink arrows in the list.
I've tried hard resets, reset of network settings and resetting of privacy/location settings - none of these fixed the issue.
the only way i have found to get rid of the arrow is to shut location services off at the master or turn off the status bar icon.....very annoying issue and a battery drain.....this is the second iphone in a row i've purchased that has had issues - iPhoneX bricked within 24hrs of purchasing last year, now this.....strike 2 for apple....
I may set up a genius bar appointment but am fearful of hearing, "you need to wipe the device and start over setting up the phone".