<p>In this paper, by utilizing the complex adjoint matrices, we transform the generalized right eigenvalue problem of the split quaternion matrix pencil into an equivalent generalized complex eigenvalue problem. This transformation enables us to propose an effective algebraic method for solving generalized eigenvalues and their corresponding eigenvectors. Additionally, we investigate the corresponding generalized right least squares eigenvalue problem for the split quaternion matrix pencil, providing a comprehensive framework for these types of problems. Secondly, we define the standard generalized right eigenvalues for the split quaternion matrix pencil. We rigorously prove that a split quaternion matrix pencil of order <i>n</i> has exactly <i>n</i> standard generalized right eigenvalues, all of which are complex numbers. Thirdly, we introduce the Rayleigh quotient for the split quaternion matrix pencil and study its fundamental properties. The definition and analysis of the Rayleigh quotient contribute to the theoretical understanding and potential applications of generalized split quaternion eigenvalue problems.</p>