I definitely feel your pain. I recently got a Pixel and the "flaky" GPS was driving me crazy, nearly causing me to get into fender-benders. But on a Reddit forum I think found the solution that also won't totally drain your battery all the time. Of course, Google had two simple ways to avoid this "feature" from becoming a bug - either return the control over location services to the phone owner AND/OR provide the option to turn off Battery Optimization when charging (as you can easily do while driving).
I don't think you have to turn off Battery Saver. Instead you need to turn off "Battery Optimization" for the specific Apps you want to be able to access GPS while Battery Saver is active.
In Pie:
go to Settings.
tap "Apps and Notifications"
tap an App that needs GPS even when on Battery Saver - say, Maps.
scroll to bottom and tap "Advanced"
tap "Battery"
tap "Battery Optimization"
In blue bar near the top, tap the "V" then select "All apps"
Again scroll to the App that needs to have Optimization turned off.
Click the app and select "Don't Optimize" then tap "Done"
Repeat those last two steps for any apps you want to have GPS access while Battery Saver is active.
When you have changed the optimization for all the apps you want (you may find some are set to "not optimized" that you actually did want optimized, for example, some social media apps), you can close out of Settings.
NOTE: I have done the above, but haven't field-tested the results. I will try to update with how it worked.