This is quite possibly the worst system in the game, and has been in a state of neglect for the game's lifespan despite all of the many, many problems with it.
On the surface it's a fine system: get world knowledge then talk about that knowledge to get MORE knowledge and some bonus quests. But in reality, many, MANY NPCs are LITERALLY (as in the correct use of the word: LITERALLY) impossible to gain Amity with through the conversation system because their range of random "Favor" ratings is WAY above the "Favor" ratings of their conversation topics. So not only can you not gain any Favor from the topics, which affects how much Amity you recieve at the end of the minigame, but even the "combo effects" of some of the topics are completely meaningless because they STILL won't result in the topics have (improved) Favor ratings above the NPC's threshold to get even a SINGLE point of favor.
It makes the whole system feel completely randomly generated with no Quality Assurance put into it to ensure that the Conversation minigames are meaningful. It's like no one took a look at, say, Quina, the Trade Manager in Altinova, and realized that her Favor rating randomly generates between 31 and 38 but ALL but one of her conversation topics cap out at a Favor score of 28. Even the "combos" you can get don't increase the Favor ratings of the topics past the threshold, and even if they did they would affect one or two topics AT MOST because for some terrible reason they go into effect MANY turns after the combo topic instead of immediately!
Also, please just ELIMINATE the "Fail to spark interest" requirement. I'm here to gain Amity, not to do things that specifically prevent me from gaining Amity. Don't create minigame objectives that are hostile to the main goal of the minigame -- that's VERY poor game design that simply leads to player frustration with zero added benefit.
This system is LONG overdue for an overhaul, but you can stopgap the problem by just cutting all NPC Favor thresholds in half, allowing players to gain Amity at a reasonable rate. Right now, the most efficient solution to Amity is to spam "Greet" at an NPC for 5 minutes, which is both boring and bad gameplay.
I wish I could bump this to the top until someone reads this who can actually do something about this. I wouldn't mind the amity game, at all, really, if it wasn't this utterly broken. But from what I've seen, PA doesn't have a history with listening to player feedback. Or ever fixing things that fall outside of class design. They simply do not care and have proven this consistently.
This is genuinely the one thing I wish they'd look into. But my hopes are just about non existent. Whenever anyone posts actually good feedback, like you did here, it's either ignored entirely, because let's face it, apparently this is a niche and the majority of the player base cares about as much as PA themselves, or someone posts something along the lines of "just spam wave". Which is just a crappy solution. Yes, it works, but it ignores something that is fundamentally broken and could be fixed if only the right people cared enough to do so.
As a rule of thumb, 90% of the time when certain topics of interest are involved, for example anything in Academics - and definitely in higher areas, the amity game is flat out not worth doing.