Jim,
The Baudot system (1874) was inherently time division multiplex. He used four five-key keyboards. They were sequentially connected to the line by a distributor. A synchronised receiving distributor separated them and sent each to its own printer.
In 1901 Donald Murry Developed the code we use today.
The start-stop system was not invented until 1907 by C.L. Krumm and H. Krumm
and eventually Teletype Corporation was born.
Download navships 0967-255-0010 from Nick England's site. You will learn more than you ever wanted know about Teletypes. It is fascinating reading.
Tom N3CRK