Locating exterior ground rod?

A ground rod often has a steel core and may be locateable with a ferrous metal detector. It seems reasonable to search based on the length of the exposed wire. Is there evidence that the wire segment was connected to the rod - or might the wire have been broken "in the middle?" Depending on how the break occurred, if mid-span, the other piece of wire might have been displaced or even removed. Also, a ground rod can be completely buried under any depth of soil.

Depending on your soil the work of installing a new rod might be non-trivial but the new rod itself should cost less than US$15. Replacing the rod seems like an economical solution.