Schala is the original owner of this pendant.
The pendant is made from ancient red rock called Dreamstone (aka Red Stone in Japanese version) which was highly valuable in prehistoric times (65000000 BC).
Throughout the game this pendant is referred to as Dreamstone, Red Stone, Red Rock and Ruby.
According to Masa, only one pendant was made along with a knife out of this ancient red rock.
The pendant was made by Belthasar and it was was experimental in time-warp technology.
The knife was made by Melchior, who also re-forged the Masamune (using more Dreamstone gotten from prehistoric times).
The Mammon Machine was also made from the same red rock.
Schala's pendant absorbed energy directly from the Mammon Machine, which in turn amplified her powers and allowed her to activate it.
When she chants to use magic, the pendant glows.
The true purpose of the pendant was unknown to her, but it opened sealed doors, such as those with the logo of the Mammon Machine, granted access to various places, and unlocked chests with ancient family heirlooms. It also opened doors in the future (after Lavos) which had to do with Balthasar, and reacted to warp devices in general (like Lucca's transporter). The Ruby Knife's purpose was simple, it was given to Crono by Melchior so they can try to destroy the Mammon Machine, which also was made of Ruby.
This pendant is a protector and it worked like Gaspar's Chrono Trigger aka Time Egg, which was used to save Crono.
In life-or-death situations, the pendant would rewind time a little, sending the owner into a safer point in the immediate past.
This happens to Kid in CC, however, nothing like this ever happens to Schala in CT.
Maybe having the pendant "powered up" affected that. The pendant seemed to do more harm than good to its bearer in CT (see Marle's experiences) anyway.
The pendant does seem to have a mind of its own in CT. In one scene after Crono's death, the Earthbound Village Elder found the pendant at Marle's side "like a guardian". Epoch also "followed" them, both could have to do with Belthasar, but I wouldn't give it much thought.
One thing is made obvious in CT, it's that Princess Nadia Guardia inherited the same pendant, as there was "only one made". In the unaltered timeline (before the events of Chrono Trigger) it was passed down through generations of royalty.
In the altered timeline Schala uses the last of the pendant's power to save everyone, so it's with her when she is stuck with the Lavos Mammon Machine. According to later Chrono series games, at some point Schala sends a daughter-clone along with her pendant into another dimension. Some time after Crono and Marle's wedding, Lucca finds a baby wearing the pendant and raises that child, making her family house an orphanage.
Kid's star coloured medicine/amulet bag aka astral amulet aka pendant, is also a confusing little bugger.
It's pictured as a bag with the Zeal crest and colors, but it's described as a small, star colored talisman.
Inside this pouch is also another Time Egg and likely the pendant, all of which protect Kid.
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