This article studies the event-triggered stochastic synchronization problem for neutral-type semi-Markovian jump (SMJ) neural networks with partial mode-dependent additive time-varying delays (ATDs), where the SMJ parameters in two ATDs are considered to be not completely the same as the one in the connection weight matrices of the systems. Different from the weak infinitesimal operator of multi-Markov processes, a new one for the double semi-Markovian processes (SMPs) is first proposed. To reduce the conservative of the stability criteria, a generalized reciprocally convex combination inequality (RCCI) is established by the virtue of an interesting technique. Then, based on an eligible stochastic Lyapunov-Krasovski functional, three novel stability criteria for the studied systems are derived by employing the new RCCI and combining with a well-designed event-triggered control scheme. Finally, three numerical examples and one practical engineering example are presented to show the validity of our methods.