Let \( \mathcal W_n \) denote any of the three families of classical Weyl groups: the symmetric groups \( \mathcal S_n \), the hyperoctahedral groups (signed permutation groups) \( \mathcal S_n^B \), or the even-signed permutation groups \( \mathcal S_n^D \). In this paper we give an uniform construction of a Hamilton cycle for the restriction to involutions on these three families of groups with respect to a inverse-closed connecting set of involutions. This Hamilton cycle is optimal with respect to the Hamming distance only for the symmetric group \( \mathcal S_n \). We also recall an optimal algorithm for a Gray code for type \( B \) involutions. A modification of this algorithm would provide a Gray Code for type \( D \) involutions with Hamming distance two, which would be optimal. We give such a construction for \( \mathcal S_4^D \) and \( \mathcal S_5^D \).