When I use PCA, I follow a few typical steps. First, I would apply PCA to the covariance matrix, I would then designate certain eigenvalues as dominant or significant (such as by those that contribute up to $x\%$ of variance or by RMT), and then I would identify the eigenvectors that match up with those significant eigenvalues.
I think you're with me at this point. It appears you want to know how to determine which of the inputs to the covariance matrix match up with the eigenvectors (i.e. how much does year $Y$ contribute to eigenvalue $N$, in your example). One way to make that determination is to square the eigenvector $N$. This squared eigenvector should sum up to $1$. Thus, you can consider each of these squared values like a percent of contribution to the eigenvector (and thus the eigenvalues). For your example, you could plot these squared values against the years for each to get a sense of how it changes as you change eigenvectors.