I searched for "or even like taking a" on Google, and I got results like these:
Sometimes that work looks a lot like staring blankly at the page, or even like taking a long walk with the dog.
The word ethics can sometimes seem overly philosophical, or even like taking a moral high ground.
Grammarly's blog states that you should add a comma before or if what follows is an independent clause. But as you can see in the examples, what follows aren't independent clauses (almost every result has a comma).
Why was a comma added in these examples?
Note: Because of this, I'm not sure whether to add a comma here:
He didn't feel dirty, or even like taking a shower.