Tentaculites fossils look like minute ribbed ice-cream cones a few millimeters in length. Typically black in the surrounding grey limestone, they are easy to overlook.
See them below the knife?
Here's a close-up (I wet the slab to make them easier to see)
Tentaculites fossils are known from the Ordovician, Silurian, and Devonian Periods (different species). The ones at Thacher Park are in the Manlius Formation limestone which formed during the very earliest part of the Devonian Period (roughly 416 million years ago) in a shallow, subtropical sea (Helderberg Sea).
The interesting thing about Tentaculites, other than it's cool to find them, is that no one really knows what they were since they're extinct today and all we have preserved is the shell without any hint of their soft parts. All we know for sure is that they belong to kingdom animalia. While most paleontologists believe they're a type of mollusk (phylum mollusca), a few others have argued that they're a type of annelid worm (phylum annelida) or even brachiopod (phylum brachiopoda). Those who argue for a molluscan affinity aren't sure if they're a type of marine snail (class gastropoda) or a squid-like mollusk (class cephalopoda).
Whatever they were, there were a lot of them swimming (crawling? burrowing?) in the Helderberg Sea which covered New York 400 million years ago. Plentiful at Thacher Park, I've also collected excellent slabs covered with them from other areas in the Hudson and Mohawk Valleys. Often we think of these types of now-extinct animals as being unsuccessful since they're no longer around. But many of them existed for millions of years, far longer than our species - Homo sapiens - which has only been on Earth for a paltry 200,000 years.