i have transoms over all my doors from the hallway. mine have no latch etc just position manually. you may have a different kind. mine are circa 1932

Crown City.
Follow link.
Pricey, but the best.
Casey

Here is a link that might be useful: Crown City Transom Hardware p. 1

Van Dyke's or Restoration hardware might have it, as well.

Both the house I grew up in and the house my Mom now lives in (1880s and 1903, respectively) have transom windows.

All of them have operators, a long push rod that attaches to the door casing. You push/pull on the rod to open/close the transom, no pole needed, and no chain needed.

From what I'm finding on the web, though, those units are expensive.

Here is a link that might be useful: This place has the transom pole hook and latches

I'd also check Wm. J Rigby. He has tons of old house hardware.

Here is a link that might be useful: Wm J Rigby transom hardware

I found a good operator at House of Antique Hardware in brass or antique.

Here is a link that might be useful: transom window hardware