For all passages, I try to keep track of both an opinion AND the main idea. You're right, some passages don't have an opinion. Usually for passages that you recognize as not being an opinion passage, you should first recognize this after reading and then when you confront a tone question about the passage, you know that the author's tone is an neutral one so most likely answers will get in line with this. I also find that some questions (either Kaplan or TPR likes to do this i forgot which), knowing which side of an argument the author is on helps to eliminate answers too. Like, I would eliminate an answer because I know that the author wouldn't agree with it.
But also, when a "claim" is usually made in a passage. There are hints of bias or opinion in disguise. It all depends on how the passage is written in my opinion. A claim could be made to sound neutral and then supported with evidence or examples, but this claim would actually be biased in my view due to the author's fine choice of words like certain adjectives. But then again, there's that fine line of recognizing if the author is just spitting out facts and describing something or is arguing with some biased intent. I'm sure such a distinction is something the test writer would love to test you.
So, from what I see, the questions come directly from the passages so if you have an opinionated passage, certainly it opens doors for questions to ask about opinion and purpose, etc. But if you have a non opinionated passage, certainly there could be questions that want to see if you can spot the passage as being neutral. Or maybe you won't even have a tone question at all and be asked all specific stuff or if I was a test writer and was really mean, I'd put in alot of convoluted info in the passage and then ask for the consistency of the information. Ex. A goes with B, C goes with D.