I've never ridden a horse with a trot so comfortable it was comparable to a gait. If your horse is smooth, I'm 99.9 percent sure he's gaiting. If whatever gait he's doing is smooth, you're comfortable, and he's comfortable, all is well! If you could get a video of us, we could help you out further. Some of the people around this forum have a lot of gaited horse knowledge and can make sure you're riding him in a way his best gaits can shine through.
I went to a horse show and a knowledgeable person showed me how to tell and how to ride. Now I can tell and each of my gaited horses need to be ridden differently to get them to gait. If they are ridden improperly they start to develop different muscles and they can loose there gait.
I have no idea about paso finos but when riding a peruvian I listen for pucca pucca pucca and a walker I listen for there hooves to fall to hunk a meat and 2 potatoes. It works.