After receiving the brass gear is it supposed to take several days for the next step in the mission to trigger? I've had it about a week now and have spoken to every character with none of them talking about it. Is the puzzle just deeper to solve?

try to give it to the person who asked you to order it?

The night I received the part I put it in storage as it was past business hours. Took it back out in the morning to try to proceed. I've spoken with every shop owner and all 10 towns folk. Tried dropping it on them before during and after their normal conversation, I only get message 'you cannot drop that'. One of my towns folk has had odd conversation since I got that piece. With first mayor he began to have no daily requests, would give me a 'token of friendship' then randomly follow me around wanting to talk then having a random conversation. A couple days ago my 2nd mayor took over and that towns person will now ask for his daily item, it won't 'save' to the to do list or as a request when speaking with him and no thought bubble. I'm guessing he was my target person and since it got stored it messed up the pattern maybe.

Some of the discolored apples are worth $100!

I've found that when I use my shovel to dig up holes, I drop veggie seeds and then I have a food source and the hole will fill on its own when the veggies are done.

I pulled the odd flower, gave it to someone - then they showed me a special spot in the ground - then the curator said something about leaving and that's all I remember! Nothing came out of the event, so I know I've forgotten something important!

I followed through with the kite, the gear, waited two days for them to order the part, and then brought the part to the shopkeeper. I don't remember what happened afterwards!