Could anybody show a paper of available book where the truncation error of the odd-even hopscotch method is properly calculated?

In their original paper, Gourlay (Hopscotch: A Fast, Second-order Partial Differential Equation Solver, 1970) didn't actually do that, only derived that it is at least first temporal order (despite the title of his paper). This is treated as a fact in the book of Evans (Systolic Algorithms, p. 228).

However, in numerical experiments, it always behaves as second order, i.e. the global error decreases with the second power of time step size.