It is not possible to make the non-primary admin node a primary.
However, the non-primary admin node can be selected to be the preferred sender of email alerts and AutoSupports. And in case the primary admin node is the preferred sender of such notifications, upon failure the non-primary admin node will automatically start sending email and AutoSupport notifications.
The main function of primary admin node that the non-primary admin node(s) cannot take over today is maintenance activities such as upgrades, expansions, decommissions, etc..
Outside of maintenance activities, both nodes (non-primary & primary) hold the metrics, audit logs and manage alerts and notifications.