In one way this is a simpler problem, reflection-wise, than the Nativity star. Christ goes up the mountain with three Apostles and is transfigured before
them (Matthew 17:2):
his face did shine as the sun: and his garments became white as snow. Various French stage directions give instructions for this (see my article). He puts on
a gilded mask and gloves (Jean Michel Mistere de la Passion), and could be wearing the white garments under his traditional dark red gown. Michel also suggests that he should be standing
in front of a vng grant soleil a rays bruny, 'a great sun with polished rays'. In my model the sun is made to rise behind Christ by a winch.
All this would pick up even ambient daylight, but for a really dazzling effect (It marres my might,
I may not see York 23:87), you could use a supplementary reflection. The stage directions from Revello (c.1490) suggests a polished [brass] basin.
The principle is the same as in the spotlight in the Nativity.
The special effects are not over, however. After the appearances of Moses and Elijah, a shining cloud descends and conceals Him and them. The voice of God speaks out
of the cloud, and when it lifts again, everything is back to normal; the brightness has vanished, and so have Moses and Elijah.
I tried this out on a scale model (12:1) of a possible reconstruction of the pageant. Photographs are below; video to be added. (Scroll down to see all