As I said, I had not known about this, and now I am in a real "look what I found" mode. 😇
First, Saint Sebaldus. Like other early Anglo-Irish missionaries to Germany and other regions, he was eventually venerated as a saint. His burial place became a pilgrimage destination in the Middle Ages, in this case Nuremberg. Like Saint James and other saints, he is often depicted as a pilgrim, with pilgrim badges on his hat. Nothing specific, it can be a Saint James shell, a Vera icon, the keys of St Peter or any of the many other motifs.
The painting on the left shows three pilgrim badges on Saint Sebaldus' hat. The one in the middle is a "mirror badge", apparently an Aachen badge. Of course, Sebaldus was not a pilgrim to Aachen or to Rome or Santiago for that matter. These paintings show us the pilgrim badges that were worn by medieval pilgrims themselves and provide an insight into the medieval world and mindset.
The painting on the left is even more intriguing; unfortunately it comes without any explanation about what's shown on the pilgrim's hats. Apparently, pilgrims sometimes just caught the wondrous light rays from relics with the help of a small mirror that was not incorporated in a decorative small metal badge, and the mirror itself became the souvenir or amulet or carrier of healing powers (or whatever we want to call it) to take home and to treasure. And to me the item on the hat of one of the three pilgrims on the right looks exactly like such a small mirror, doesn't it ... ?