No, you don't, Brights increease EXP, and unless you are synthesizing someting else to get the EXP, you shouldn't anything for the Ultima Weapon. However;

Bright Stone:
Aeroplane (Timeless River)
Cannon Gun (Space Paranoids, Coliseum)
Driller Mode (Coliseum)
Luna Bandit (Agrabah)
Silver Rock (Agrabah)
Tornado Step (Coliseum)
Wight Knight (Holloween Town)

Also, I included a post to my Working Thread, which has multiple guides to Synthesis, and Bestiary included.