People have been saying that there is no such thing as a random move-in for the 10th plot but I'm not sure if it's confirmed.
I do know that even if you can't get a random, you can pick someone up from someone else's void (not sure if this is intended or not) so if you have an open plot I recommend you try to fill it asap with an invite.
Random move-in are totally possible and will most likely happen on the day after you've built the plot. I built the plot, did some villager hunting on mystery island tours (4-5 tickets IIRC), and did not find any villager I wanted so I did not invite anyone. The day after, the plot was sold to Snooty. She moved in the next day.