I have a 1G Samsung T5 that I would like to partition into 2 partitions so I can use one of them for Time Machine backup. However the Partition button in Disk Utilities is always grayed out for the T5 disk. It is not grayed out if I select the Machintosh HD. What do I need to do to partition the T5? (I am running newest MacOS).
You cannot partition a volume. You must partition a drive (device). To do so, click on the drive itself, located just above the partition you selected on the sidebar ("Samsung Portable...").
Then, you can partition the disk.
Edit: Back all data you want to keep up and Erase the disk as GPT (GUID Partition Table). Newer versions of DU for some reason don't want to work with MBR partition tables. Choose ExFAT as file system to be able to read and write to the disk from both Windows and macOS, or APFS if you only use Macs.