What is a proper and appropriate response for a Buddhist when someone near them sneezes to show that you care about that person’s health and well-being?
There is no right or wrong answer to this. Sneezing is actually a healthy response to expel irritants from your body. It can be an indication of an unhealthy state too.
When we sneeze, we usually apologize to acknowledge that we may be spreading disease or disrupting a quiet setting. So this interaction goes both ways.
My understanding is that the phrase “bless you” or “God bless you” was said because it was thought that a sneeze caused someone to expel their soul from their body. So it was said as a protection against this.
The conventional meaning of God as a creator who answers our prayers and the existence of a permanent “soul,” however, is contradictory to Buddhist thought. But if we think of “God” as pure love, compassion, and wisdom that permeates the universe for the benefit of all sentient beings— in essence, Truth with a capital “T”—we call this Amida Buddha.
Another common phrase is “Gesundheit,” which is the German word for “health”— meaning “I wish you good health.” But really any response to acknowledge someone’s sneeze is a way to show you care about that person’s health. Using “bless you” has religious connotations but is showing politeness and manners. I don’t think you need to overthink what is appropriate. You may be able to come up with a creative way to do this.
Gassho, Rev. Todd