When to put a comma before participial phrase

This site is excellent. Thank you! A Japanese colleague of mine recently asked me to explain to him the rules about comma usage in the following two sentences (taken from an English textbook):

"He always eats breakfast reading the paper."

"She was making sandwiches, talking with her daughter."

I've been Googling participial phrases and comma usage for hours, but have been unable to find a satisfactory answer. I know that the comma is omitted when the noun modified by the participial phrase comes directly before the participial phrase, but what about the first sentence, above? Is it a question of restrictive vs. nonrestrictive elements? Or is the textbook example wrong? A comma in that case seems wrong to me, but sometimes, when it comes to grammar, the more I think about something, the more difficult it becomes to figure out the proper choice.

Thanks in advance!

Solution 1:

The primary difference in the forms of the two sentences is that the first one has "eats... reading..." and the second one has "was making... talking..." It thus seems that the first sentence—punctuation aside—can be read only as signifying

He always eats breakfast [while] reading the paper.

whereas the second sentence—again, ignoring punctuation—can be read as meaning either

She was making sandwiches [while] talking with her daughter.

or

She was making sandwiches [and] talking with her daughter.

So perhaps the comma is there to signal a dropped and and to emphasize the parallelism between "making sandwiches" and "talking with her daughter," both of which attach to the word was if an implied and is at work. I certainly don't see the argument for putting a comma after "sandwiches" in the second sentence as being any stronger than the argument for putting one after "breakfast" in the first, if the point is simply to mark the absence of the intended word while in both cases.

Still, I'm at a disadvantage in trying to work out the book's reasoning because my preference would be to include the missing while in the first sentence and the missing while or and in the second sentence—and if you do those things, neither sentence needs a comma.