Big issue, of course this is why a large number of judgements never get paid, You can hire a PI to try and find it.
Have a friend or someone send them a 10 to 20 dollar check for some "reason" if they deposit it, then it will show bank numbers.
Ask for the numbers though the court. ( of course they will empty them at that point

You shouldn't need the account number; merely the bank and preferably the branch.

This varies by location. Some courts will require that have you full info on the account before issuing a writ of execution, others will issue one with minimal info. I would suggest you talk to YOUR bank and ask what info they would require to process a writ of execution.