Yeah it's important to see Trico as a coop partner instead of some dumb NPC bot. His behaviour is often an integral part of the puzzle, story progression, and the emotional narrative. If something catches his attention, or he found something related to the puzzle, he's expressing it with sniffing, vocalizing, looking at it, and mostly it's the animation that speaks the most.
It has similarities to the usual coop NPC except Trico doesn't say "Nathan, I found a ladder. Give me a boost!". Sometimes it's obvious, like he will be afraid of something, the hint system ("hold L3") will give you something like "XYZ is making Trico panic, you have to find a way to calm him down". Or the other way around something smells good and he'll try desperately to reach it. The rest of his behaviour is more subtle, but mostly he's reactive to either you or elements of the environment.
It's not randomness. The basic aspect of "coop with an NPC" is still there, triggers from gameplay are still there, it's just more credible here because there's a lot more work put into it, more than any game I can remember. Same concept, much more elaborate implementation. You can certainly predict Trico's behaviour if you pay attention to the details, it's a central part of the game. If Trico was random it would be a really stupid game, and if he was a simple robot NPC executing order the narrative wouldn't work.