To address the insufficient accuracy and stability of inverse kinematics for a six-degree-of-freedom manipulator in automatic operation of electrical cabinet components, a black-winged kite algorithm integrating elite-guided Gaussian mutation, fractional-order historical memory, and Cauchy-Lévy hybrid perturbation is proposed based on the M-BWKO framework, namely GFL-BWKO. The proposed algorithm constructs a fitness function incorporating position error, orientation error, wrist-center error, and joint-limit penalty, and coordinates position approximation and orientation optimization through dynamic weighting. Gaussian mutation, Grünwald--Letnikov fractional-order historical memory, and Cauchy-Lévy hybrid perturbation are introduced into the attack and migration behaviors to enhance local exploitation, global exploration, and the ability to escape from local optima. Simulations and physical experiments are conducted on a JAKA Zu5 manipulator. The results show that, compared with M-BWKO, GFL-BWKO reduces the mean position error, position error standard deviation, mean orientation error, and orientation error standard deviation by 37.65\%, 23.65\%, 5.86\%, and 19.47\%, respectively. Physical experiments further verify the engineering feasibility of the proposed method.