I think that under any circumstances, Rita's external should have no less than two partitions: one, because Rita should have a clone, no matter how far behind the times it is, and a second for potential Time Machine or other use.
I won't argue with you but it goes against my grain to use partitions. I wish it were possible to use APFS volumes instead of Partitions, but Time Machine rules that out.
How about a 128GB partition for the clone and the rest of the drive for a future Time Machine backup?
That works. Since Rita's got a 1 TB external drive and only a 120 GB internal, there's no way she'll ever run out of space in either partition. (And I doubt that there's any way she'll ever run Time Machine, anyhow.)
The possibility of running out of space in a partition, which is, correctly, at the root of your dislike of partitions, isn't in play in this instance.
