Rattling eyelets are common especially after a wheel is built and unlaced. The eyelet is fitted from the tire side of the rim and the rivet head formed on the rim side to prevent it from falling out. This is true for both single and double eyelets. When the wheel is built the nipple forces the eyelet a bit deeper and settles the head into the curve of the rim. This can create added slack and the eyelet will rattle if the pressure is removed.

The effect is most common with double eyelets because these are toleranced to hang from the upper edge rather than press against the bottom surface. Otherwise they couldn't serve the purpose of transferring load to the upper surface. When the wheel is built the eyelet is pulled forward settling the eyelet lower pulling the upper surface down with it. Often a close inspection of a built double eyelet rim will show that the rim side of the eyelet is pulled well off the rim's surface.

In any case, if an eyelet somehow manages to rattle on a built wheel, it's telling you that it's spoke is slack.