Sometimes it depends on what the gate agent "sees". A few weeks back on a US domestic flight I had my standard purse (not large) and a small roll-aboard bag I've used for quite a while, mainly for overnight business trips in the US when I still lived/worked there. I am well familiar with the rules and even the various aircraft, and this bag fits underneath the seat on even the smallest puddle jumpers.
The person in front of me did NOT have a 'gate check' tag on a huge (by comparison) wheelie bag that would have been fine on a full size 757 or Airbus330, but definitely not on the Embraer. She also had a huge 'purse' that was larger than my roll aboard. She was unchallenged, and not told that she needed to gate check the large bag.
I was told I needed to gate check my carry-on, and when I replied that it would fit under the seat, the gate agent pointed to the purse and asked "what are you going to do with that?"......and I replied "stow under the seat or in an overhead compartment - it's my purse". She made me take a yellow tag, and lectured me that I would need to gate check if it didn't fit.
Fast forward....both my bags went under the seat and the woman who boarded ahead of me trundled from the rear of the plane with the large bag, had to ask for a yellow tag, and one of the attendants took it off to be gate checked.
Look on the website for the airline; they have pretty specific info with dimensions. I've seen backpacks brought on small flights as a 'personal item' scores of times over the years. Just try to arrange the contents so there are no large or unusual bulges that would limit placement.