The triluminaries (all three of them) originated on Epsilon 3 according to JMS. They are among the items that Zathras transfers from his ship to the White Star in "WWE". (One of the boxes is marked with the Minbari triangle symbol, but this is hard to see since none of the angles used in the final cut really highlight it. This box contains the Chrysalis device and - presumably - the triluminaries.)
After the Shadow War of the 1200s the triluminaries and the Chrysalis device are brought to Minbar. Delenn eventually takes the Chrysalis device with her to Babylon 5, and starts assembling it. During one of her visits to Minbar a member of the Grey Council gives her a triluminary to activate the machine. He assures her that it won't be missed because "there are two others."
While fans have speculated for years that the Vorlons are responsible for both the Great Machine and the triluminaries, JMS has never confirmed this, and no canonical source really goes into the origin of either.
Because the Grey Council member seems to grab whichever triluminary he can get his hands on ("there are two others") I doubt that they are either "one time use" devices, or that they are "keyed" to individuals. (Which many people seem to assume.) It is just as likely that Sinclair and Delenn used the same triluminary as that they used different ones. I don't think the fact that there are three of them is significant in the matter of Catherine Sakai, for instance.
The device clearly has multiple uses, since it is held up before new members of the Council, used to "scan" prisoners of war, and also powers (or controls) the Chrysalis device.
I think that the original notion in the back of JMS's head may have been that the triluminaries were based on parts taken from B4, or even from Sinclair's link. The rare close-ups of the thing show a metal triangle in the center of which a fairly crude-looking printed circuit affair is suspended by wires. But I think this idea was dropped as the story changed in the telling.
I suspect that this was going to be revealed as the reason that the triluminary glowed for Sinclair - that it was reacting to his DNA, having been built out of his link - by the Minbari. At the time JMS had said flat-out that Valen left had no off-spring.
I think the changes in the story created by Michael O'Hare's departure freed JMS to give Valen children, and make Delenn one of his descendants. In that case the Vorlons or Draal or somebody else could have created the triluminaries and incorporated Sinclair's DNA because they knew that would work for the two individuals who would eventually use the Chrysalis device, as well as providing an excuse for the Minbari surrender at the Battle of the Line.
Regards,
Joe