LightDM and Multiseat: how to make greeter remember the username of the last logged-out user?

I've configured a two-seat setup with Xubuntu 18.04. The only problem is that when user logs out on either seat, the greeter then picks (seemingly) randomly the username for the next login. Since the two seats are typically used by the same two persons, in most cases they have to choose their usernames before entering passwords. What I want is that on each seat, the greeter would show by default the username of the user who was last to use this seat.

Currently, the contents of /usr/share/lightdm/lightdm.conf.d/60-xubuntu.conf is the following:

[Seat:*]
user-session=xubuntu
greeter-show-manual-login=true

P.S. I found in docs how to make autologin of a specific user on a specific seat. This is not what I want. I only need to suggest the specific user on a specific seat, not to autologin that user.