я использовал вот такой вариант в одной программе
function GetScreenOffTimeout: integer;
// Androidapi.JNI.Provider, FMX.Helpers.Android
begin
Result := 0;
{$IFDEF ANDROID}
Result := TJSettings_System.JavaClass.getInt(SharedActivityContext.getContentResolver,
TJSettings_System.JavaClass.SCREEN_OFF_TIMEOUT, 15000); // 15 seconds is default is not found
{$ENDIF}
end;
function SetScreenOffTimeout(ATimeOut: integer): Boolean;
// Androidapi.JNI.Provider, FMX.Helpers.Android
begin
Result := false;
{$IFDEF ANDROID}
Result := TJSettings_System.JavaClass.putInt(SharedActivityContext.getContentResolver,
TJSettings_System.JavaClass.SCREEN_OFF_TIMEOUT, ATimeOut);
{$ENDIF}
end;