The functional properties of the whole-brain structural connectome have been investigated by embedding it into a reservoir computing model known as the echo state network. In the connectome-based echo state network, the nodes in the reservoir layer are wired according to regional structural brain connectivity. Several methods exist for converting structural connectivity weights to reservoir weights. A recent study explored the effect of introducing randomness into the conversion process when solving the standard memory capacity task. It found that randomizing the order of structural connectivity weights had little impact on performance, whereas randomizing their signs (multiplying each weight by either 1 or \(-1\) at random) led to improved performance. However, whether these findings generalize to other reservoir computing tasks remains unclear. The present study addresses this question by examining the effect of randomizing the order or signs of structural connectivity weights on performance across four neuroscience tasks implemented by NeuroGym, using the conn2res toolbox. The results show that randomizing the order of the weights substantially influences performance and randomizing their signs leads to performance deterioration. These observations contrast with the earlier findings from the memory capacity task and highlight the task-dependent nature of the effect of randomness. This study underscores the need for further research to develop a unified understanding of how introducing randomness into connectome-based reservoir weights influences performance across different reservoir computing tasks.