I would call a 5/8" spigot a 'standard light stand' mount of that approximate size (The next size up is 1-1/8"). The light stand has a spigot, the light has a socket. You can get 5/8 spigots with 1/4 or 3/8 female thread at one end.
Here is a link to a photo of what you would want to buy, in order to mount that onto a tripod's threads: a 5/8 inch spigot, female threaded at both ends. One end is 1/4x20 National Coarse, and will fit your USA-market tripod screw, the other end is a 3/8 thread, which is handy if you wish to remove the tripod head, and mount directly to the 3/8 inch thread that is underneath, and used to hold the head onto the leg set.
I was just thinking, do you think the included ball head could be detached from the L-bracket? If so, I'll bet I could attach my tripod's QR plate and secure it with a nut.