So how does one find these chests
I heard that in the distant past, you used to have to search a neighbor's city's outskirts to find them.
These days, up to three are simply handed to you at random at the instant you perform the neighborly help on a neighbor's city. In the form of a popup box stating what it is you received. I'm unsure if those helps has to be with golden hands or not. (I'll be sure to check that this coming cycle)
As
@Gkyr has stated, you can perform neighborly help once every 23 hours, so if you're a little late one day, you can slowly slide the times back earlier in the day. One day at a time. You could theoretically perform 25 neighborly help cycles in a 24 day period if you wrecked your sleep schedule hard enough.
The bit about the Moon Bear was interesting, though. It is with sadness to say that I only got four artifacts from a prior Spire cycle.
EDIT: No, it doesn't need to be golden to get an award.