The Wikipedia article on metals describes them as elements whose polyatomic configurations* exhibit any one of a number of patterns. I could not discern any property that characterized all the patterns.
To the best of my knowledge, there are two main categories of elements: metals, non-metals. There's a third category, metalloids, whose members are those that satisfy some of the criteria for inclusion in both main categories.
It would seem very odd if there were nothing that characterized all, and only, metals. In fact it would seem that metals are better conceived of as an arbitrary grouping of what is actually a number of other categories, each of which would include all, and only, the elements that exhibit a single type of polyatomic configuration*.
Is there a characteristic that characterizes all, and only, metals?
*(I'm using the phrase 'polyatomic configuration' in order to express 'the way that atoms of a particular element stick together when you have a number of atoms of that element connected together'. Is there a standard term that expresses that idea?)