Java, 408 401 396 Bytes

 public static int getPosSecondZero2(int number){ int overflow = 2^32-2; if(number < 0 || number > overflow){ return 0; } String binaryString = Integer.toBinaryString(number); char[] binaryCharArray = binaryString.toCharArray(); int count = 0; int idx = binaryCharArray.length; int length = binaryCharArray.length -1; while(count < 2 && idx>0){ idx--; if(binaryCharArray[idx] == '0'){ count++; } } if(count == 2) return length-idx; return 0; } 

Plain(effective 396 Bytes):

public static int getPosSecondZero2(int number){int overflow=2^32-2;if(number<0||number>overflow){return 0;}String binaryString=Integer.toBinaryString(number);char[] binaryCharArray=binaryString.toCharArray();int count=0;int idx=binaryCharArray.length;int length=binaryCharArray.length-1;while(count<2&&idx>0){idx--;if(binaryCharArray[idx]=='0'){count++;}}if(count==2)return length-idx;return 0;}