Intermediary bank is not optional for wire transfer. If the beneficiary bank has no operations in the country from where the wire transfer is originated, the intermediary bank is mandatory. HOWEVER, in case of AdSense wire transfer payments to India, they have said they are capable of finding the intermediary bank for most of the Indian banks. So, if you leave it blank, they will find it for you!
If the beneficiary bank has no operations in the country of origin, then they cannot make a direct wire transfer to the bank. Instead, they make the transfer to an intermediary bank in which the beneficiary bank has an account. Once the intermediary bank receive the payments from the originating bank, the payment will be further transferred to the beneficiary bank, based on the account number and other details included in the original transfer.
If you are finding it difficult to get the intermediary bank details, you can leave it blank. Let Google find it for you. However, in case of some small banks, Google may fail to look up the same and then it will become your responsibility to find all the necessary details from your bank.
Just go to your bank and they will give you all details. Make sure you tell them that the wire transfer is from Singapore, from where Google sends the wire payments to Indian AdSense publishers.