You said, "Yes, the power is connected. But, But how would that keep it from being seen in the Disk Manager? My system is a Tower, not a laptop."
1. Your system cannot "see" that drive in the enclosure if the drive unit cannot spin up and perform a normal read / write operation as it starts up. That is part of the POST process of the disk unit, and it must be able to report successful start-up to your mobo hardware. IF the power being supplied to the disk unit in the enclosure is NOT adequate, typically what you see is that the lights are on and it looks OK, BUT when it is required to actually spin the disks and move the heads, the power is not enough and it can't do that, so it fails. Thus, Disk Manger can NOT find a valid disk to work with.
2. A standard USB3 port can supply power to an attached device at 12 VDC up to 0.9 A max current. An enclosure can be used for various types of storage units. It happens you are using a 2½" SATA HDD. SOME such units are particularly designed to be able to work properly with no more than 0.9 A power supplied. Such units come with NO port to add extra power and rely entirely on the USB3 port supply. That type is always used in those complete "Laptop Hard Drives for USB3", and normally they work just fine. (There have been cases in which the USB3 port in use actually is NOT up to standard and fails to provide that minimum power.) BUT common HDD's used in many places, including desktops, are NOT designed for such low power. So when you mount one like that in an enclosure and try to use it with any USB3 port WITHOUT adding a connection to other power, the disk unit cannot operate properly. That is why such an enclosure MUST provide a separate power supply module AND a port on the enclosure to plug that in, and you must use it. If you think you are doing that, you may need to verify that the power supply module IS doing its job.