What signal tells you a design problem is a genuine fit for the Composite pattern?

Composite fits when you have a real part-whole tree structure -- individual items and groups of items that need to nest arbitrarily deep -- and you want client code to operate on a single item and an entire subtree through identical method calls. File systems, UI component trees, and organizational charts are classic examples, because in each case a leaf and a branch both respond meaningfully to the same operation, like computing a total size or rendering a layout. If the domain data doesn't actually nest, or if leaf and container objects need fundamentally different operations with little in common, forcing a shared component interface just adds indirection without buying anything -- Composite specifically pays off when uniform treatment of nodes and subtrees is the actual requirement.