Hi,
Wrong table. The trigger record located in Tasks and you are trying to update the record with the same ID in Parents, of course it not exists there

So, subsequent actions always have to tie back to the table in the original trigger? I cannot choose to perform an action in another table? If so, why is it even an option to be able to select another table?

Sorry, my first explanation was bad. 
Record in table Tasks, which triggers the automation, has it's own id (its always recXXXXX, where XXXXX - 14 random chars). ID is not visible in usual table, you can see it in the formula RECORD_ID() or in the hyperlink when you open a single record.
I guess you want to update other record in table Patient, which linked to your trigger record.
Other record has other id, which also can be acquired from the linked field of your trigger record.
it's not visible as well, the link contains visible record name (record name is a value of it's primary field)

Instead of put 'Record ID' of trigger in step 2, you should scroll down, choose linked field, then select Display and change from Name to ID

Sorry, I wasn't able to follow your solution and didn't find a way to choose "Display" in the dropdown options. However, the following, see image, ended up working.