"Are you licensed by the Town of Islip specifically?" Not "licensed and insured", not "licensed in Suffolk County" — licensed by Islip. The Town keeps its own register and its own examining board, and § 40-9A means the permit can only be issued to somebody on that list. A Suffolk County licence does not substitute here, and neither does a licence from Babylon or Huntington. It is a fair question and it is not rude to ask it.
"Who is pulling the permit, and is it going in your name?" § 40-2 requires that a Town of Islip-licensed master plumber hold a controlling interest in the business doing the work, and the code says plainly that no subcontracting or rental of licences is permitted. If the answer involves a licence borrowed from a third party you never meet, that is the arrangement the rule was written to stop.
"Does this job need a permit at all?" Often the honest answer is no, and we would rather say so. But the Town’s own list is broader than people expect: gas piping and new fixtures, an AC install whether central or ductless, a gas fireplace, a gas stove, an outdoor BBQ or fire pit run off the house gas, an oil tank going in or being abandoned, a lawn sprinkler connection, a commercial kitchen hood. A surprising number of the jobs homeowners think of as swaps are on that list.
And the reason any of it matters is the closing. Unpermitted plumbing, gas and mechanical work does not usually cause a problem while you live in the house. It causes a problem when a buyer’s attorney asks for the certificate and there isn’t one, and the fix has to happen against a contract date. Doing it on the permit the first time costs a filing fee and some scheduling. Doing it afterwards costs whatever the other side is willing to hold the deal up for.