Running Google Play Services on Android 4.1.2 is a nostalgic exercise in backward compatibility. It requires a delicate balance of holding the OS back from updating automatically while manually installing compatible legacy frameworks. If you are using this device for media consumption (e.g., an old tablet as a photo frame or MP3 player), stripping Google Play Services entirely and using offline apps often yields a faster, more stable experience.
This is written for someone trying to get an older Android 4.1.2 (Jelly Bean) device running properly in a modern environment. google play services android 4.1.2