I have a couple of comments.
1) in Image Sync -> Settings -> Background location information transmission, select an appropriate time. I use 6 hours.
2) With an Android phone (mine is a Google Pixel 4a) make sure battery optimisation for the Image Sync app is off. This is buried deep... See
K-3 III image sync bluetooth woes [Solved - Samsung settings issue] - PentaxForums.com for detailed instructions.
Note I have yet to test #2 (plan to do so today) but it seems it might account for my being back to geo-tagging only working for the first so many minutes despite #1 being set correctly. I've not changed my phone since I got the K3iii, but it has undergone several Android upgrades since then.
*if* I've fixed the problem it makes using image sync for geo-tagging easy:
1) Make sure phone is charged!
2) I turn on GPS & Bluetooth on the phone and make sure network & mobile data are turned off, to maximise battery life. It seems to take the phone a little while to 'find itself' in GPS terms
3) Turn on the camera
4) Open the Image Sync app
5) Tap the 'camera' symbol in bottom right of the screen
6) Tap 'PENTAX K-3 Mark III' (or whatever) in the list of camera types
7) Tap the 'Connect to PENTAX_999XXX' in the menu.
Job done, I hope! It was so much easier with the K3ii. Sign...