A follower's UAT left is led with leader's LH.
A follower's UAT right is led with leader's RH.
This means to do a UAT right from open the partners need to be in a double hand hold, for the leader to have RH connection.
From open position, UAT left naturally lends itself to the follower going first. The pattern then is follower's UAT left, leader's UAT left.
From open position, UAT right naturally lends itself to the leader going first. The pattern is then leader's UAT right, follower's UAT right.