Moniales OP draws attention to a fascinating observation by Fr. Thomas Philippe, OP:
In the case of a vocation to the active life, certain natural dispositions can be recognized; but for the contemplative vocation, which is the blossoming of the life of grace and of the theological virtues, there are no natural predispositions. Insofar as a call to the religious state is involved, one may speak of the absence of counterindications; but that is all.
This has obvious implications for how to go about (or perhaps how not to go about) directing people towards the contemplative vocation.
But I'd say it also has some implications for every Christian. If the contemplative vocation is, in fact, the blossoming of the life of grace and of the theological virtues, then it is a vocation each of us is called to -- or better, contemplation is a part of each person's vocation. And we can't use "But I'm not the type" as an excuse, because there is no type.