Job Shop Scheduling problems have become popular because of their many industrial and practical applications. Among the many solving strategies for this problem, selection hyper-heuristics have attracted attention due to their promising results in this and similar optimization problems. A selection hyper-heuristic is a method that determines which heuristic to apply at given points of the problem throughout the solving process. Unfortunately, results from previous studies show that selection hyper-heuristics are not free from making wrong choices. Hence, this paper explores a novel way of improving selection hyper-heuristics by using neural networks that are trained with information from existing selection hyper-heuristics. These networks learn high-level patterns that result in improved performance concerning the hyper-heuristics they were generated from. At the end of the process, the neural networks work as hyper-heuristics that perform better than their original counterparts. The results presented in this paper confirm the idea that we can refine existing hyper-heuristics to the point of being able to defeat the best possible heuristic for each instance. For example, one of our experiments generated one hyper-heuristic that produced a schedule that reduced the makespan of the one obtained by a synthetic oracle by ten days.