How to install a stained glass window, behind an existing tempered sidelight?
Your stained glass panel and frame would have to fit into the area you want to fill. Your side light should have a wood frame, so the stained glass frame could be screwed into place. However, if you don't already have the stained glass, I have a low cost solution. Go to Home Depot (or other store) and check out the window film. They sell film that looks like stained glass. You cut it a little oversized, squirt water on the glass, and apply the film to the window. Then just smooth it out and trim the edges with a razor knife. Instant stained glass window. They also sell dark tinted film to reduce heat and light infiltration or frosted look to add privacy to a window.
I have seen people who have put the stained glass in a frame and have hung it from the ceiling. These links show using it for a window
and a panel (now this link is for Amazon but it does give you the ideas without breaking the bank).
Hope these help.