Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's minimal complexity (no parameters, no output schema, no annotations), the description covers the purpose and timing adequately. The only notable gap is return-value semantics or failure behavior, which an agent would need to learn from the live response, but for a zero-config health probe this is a minor omission.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.