I noticed that when on my S60 the Gesture is Off and in Garmin Connect Mobile 3.20.3 Gesture is On, that after synchronisation both setting stay the same and the backlight on my S60 is working, but when in Garmin Connect Mobile Gesture is Off, that after synchronisation the Gesture setting on my S60 is changed in Alway On and that the backlight of my S60 is not working anymore. Conclusion in the Dutch version of the Garmin Connect Mobile software the On (Aan) and Off (Uit) are switched. Probably it is only a translation error or otherwise a software bug.
The problem is solved with the update of a new version of Garmin Connect Mobile for Android 3.22.0.1 and now the backlight settings stay the samen and the backlight is everytime activated by tapping on the screen.