System project pods node affinity


We have AWS cluster with two worker node pools. On node pool has nodes labeled as test nodes and we shut them down outside working hours. Some system pods are scheduled on those nodes and after their shutdown some services are therefore unavailable.
Is there a possibility to set node affinity for system pods? I know I can define those rules manually but I don’t want to change those settings manually. I tried to drain nodes but those pods have toleration for NoSchedule and NoExecute taints.