This general rule, also known as the "Mohawk Doctrine," has been around for quite some time; in fact, as noted by New York State's highest court, the origins of this rule are traced back to English common law:
" '[A] man may not derogate from his own grant; the vendor is not at liberty to destroy or depreciate the thing which he has sold; there is an implied covenant, on the sale of good will, that the vendor does not solicit the custom which he has parted with; it would be a fraud on the contract to do so. . . . It is not right to profess and to purport to sell that which you do not mean the purchaser to have; it is not an honest thing to pocket the price and then to recapture the subject of sale; to decoy it away or call it back before the purchaser has had time to attach it to himself and make it his very own' " (Von Bremen, 200 NY at 50-51, quoting Trego v Hunt,  AC 7, 25; see also Mohawk, 52 NY2d at 286; Bessemer Trust Co., 618 F3d at 86).
Granted, the language is a bit dated (then again, this was written in 1910), but the message is clear: you, as the seller, don't get to have the benefit of being paid for your business if you have no intention of actually conveying it. It would be a clear violation of fiduciary duty.
Interestingly - and importantly - the Court of Appeals took this concept further, stating:
A seller's "implied covenant" not to solicit his former customers is "a permanent one that is not subject to divestiture upon the passage of a reasonable period of time" (Mohawk, 52 NY2d at 285). Indeed, we have recognized that upon the sale of "good will," a "purchaser acquires the right to expect that the firm's established customers will continue to patronize the business" (id., citing People ex rel. Johnson Co. v Roberts, 159 NY 70, 80-84 ). This is so because "[t]he essence of [these types of] transaction[s] is, in effect, an attempt to transfer the loyalties of the business' customers from the seller, who cultivated and created them, to the new proprietor" (id.).
In other words, even if the agreement for the sale of the business doesn't spell this out, you, as the seller still can't solicit the clients whose goodwill you just sold to the purchaser. Moreover, your ban on soliciting these customers is not bounded by time. It's forever.