While I cannot speak for Long Island, it is typical practice to have a listing agreement to represent a seller (seller's agent). An exclusive right to buy, aka buyer rep agreement, is a fairly standard practice and is even required in some states.
A buyer rep agreement defines the ways in which your agent will work for you and you can typically add stipulations to that agreement including that they actively search for FSBO properties, etc. Keep in mind that if NY is a state that does not REQUIRE these agreements, it may not be a bad idea to check with a few other buyer agents. Checking out the REBAC website (rebac.net) and find an ABR (Accredited Buyer Rep) or just look for someone that has ABR on their card :-)
The ABR means they took a few extra classes on dealing with buyer related issues and may be slightly more qualified to help you if a buyer rep agreement is necessary.
Agency relationships also vary from state to state, but you can see a very basic overview of agency relationships by visiting one of my blog posts about them (in web reference below)