An example method of executing a periodic task of a service having service instances replicated across hosts in a cluster of a virtualized computing system, the service instances executing in pods implemented by virtual machines (VMs) on the hosts, the method including: persisting, by ping tasks of the service instances, records in a pod information table of a database, the records including pod identifiers of the pods and leader indicators; determining, by a first ping task, a leaderless condition in that the leader indicator in each of the records is false; setting to true, by the first ping task in response to the leaderless condition, the leader indicator in a first record having a first pod identifier for a first pod in which the first ping task executes; and executing the periodic task in the first pod to the exclusion of each other of the pods.