Good Day!
For those who, like me, had an issue while switching between applications using the "start the game and then switch to fake GPS, and then return to the game" method because they have a Xiaomi phone with MIUI, I want to share the alternative method I found to use fake GPS and prevent the closure or restart of background applications:
1. Make sure the game has turbo videogames enabled and its in list.
2. Start the game.
3. Swipe from the top right to the center with your finger to open the turbo videogames menu.
4. Select the fake GPS application from the recent apps menu.
5. The fake GPS application will now open in a bubble screen, so there's no need to switch between apps, as you can do everything on a single screen. Start fake GPS using your current location.
6. Have fun and remember not to abuse cooldowns or move too fast on the map.
However, I still believe that a serious mod remains necessary to stop avoiding being slaves to external allocations like fake GPS.