Author here. I think "looking" is indeed not the right term for this.
Most problem discovery in any market happens through careful qualitative analysis that happens during and after interviews with prospective customers.
Looking at their behavior is a first step to getting a glimpse of what the day-to-day work looks like, and where you as a SaaS could interface with that.
The second step is figuring out customer intent ("what do I want to get done"), problem awareness ("what could be done much better"), pain intensity ("what is unbearable about my work").
Some of those come directly from the prospect, mostly problems where they have high pain and high awareness. Others, you will have to find yourself, such as low-awareness problems. Then, there are problems to dismiss, such as low-pain and non-intent-aligned ones.
To me, a niche represents a group of people you select out of a more general population.
From what you wrote, I understand that we agree that niches don't "exist", they are "defined". That is both a result and a starting point, which makes this whole exercise so hard - it's an iterative approach: you define a niche, you explore their problems, you re-define the niche, explore again, until you have found a critical problem worth solving.
The point is that you can't find problems without communicating with those who have them. Looking won't do. You will need to listen.