When you re-equip the ring, it puts the on-use effect on a 30 second CD.
If you re-equip it right before pull, and the rest of your raid uses ring immediately, can you still use your OWN ring after 30 seconds? This would allow you to use your ring personally rather than tied to the rest of the players' rings, as long as you use it on CD (so your ring CD is always offset from the raid group's).
On some bosses, they are reaching 20% right after the ring buff expires. If I can delay my own ring by 10s or more on pull, it would let me use it during execute range for some bosses.