cheap 3.7GB Universal Serial Bus (USB)
Could be a clue. There are reports of some cheap USB thumb drive not being Mac-friendly. Does it have a brand showing? Did the thumb drive ever work on that Mac in the past? Tried it on any other Mac?
What does Disk Utility report for teh formatting of the thumb drive?:
Can you confirm what kind of eMac you have? Early models had USB 1.1; later ones had USB 2.0. Some cheap USB drives can't clock back to USB 1.1.
Please use this Apple article to indentify what eMac variant you have by serial number, but DON'T post your serial number here, just the eMac Model name you find in the chart:
Should you face a situation where you need to erase a USB quickly, instead
of using Disk Utility, just drag all the content you do not want to the Trash,
and Empty it before you eject the USB flash drive or other device.
By dragging only the content to Trash, and Empty, you do not need to reformat.
This saves some time/trouble. Sometimes you may have to reformat one of
these, from my experiences with cheaper ones, by then they may have failed
already and don't know it yet.
Even though the older eMac has USB1.1, later has 2.0, even a Drag to Trash/
Empty may take a little time; but no where near the time it may take to attempt
to erase using Disk Utility.
A USB flash drive nor a SSD should ever be secure erased and some makers
say not to do it (where zeros overwrite content) as that isn't good.
If you are the only user of a flash USB drive or thumbdrive, then the fast way is
the best. In the case of a cheap and non-durable one, you could physically
destroy it when done; if it doesn't do that all by itself.
Hopefully the adventure has been worthwhile...