Ethos is defined in different ways, but it is basically the credibility in terms of style, tone and characterization that is used by the writer to convey his work upon the audience.
Tennessee Williams conveys his work effectively through the use of the following techniques a) an actively involved narrator in Tom Wingfield, b) in using specific symbols to set the atmosphere of the times (economic limitations, desolation, and change) and , c) in creating characters who are stereotypical of their time and place but whose inner struggles are quite universal.
The effectiveness of Tom as a narrator comes from his ability to explain some of the symbolism in the stage directions. For instance, this is how we realize that the fire-escape is a symbol. He also foreshadows the behaviors of the rest of the characters which is a highly convincing tool to explain to the audience "who is who" in the play.
The symbolism in the stage directions makes us understand the struggle of the family: a struggle to move forward, and to let go of the past. It also puts the play within its proper historical context
Finally, the ethos comes through in Williams' successful portrayal of characters to whom the audience can connect: Tom as a frustrated man who is trapped with his family due to his sense of duty; Amanda, the equally-frustrated abandoned wife who has to make due for her children but will never renounce the memories of her richer past; Laura, the young and socially-anxious woman who, at 26, still thinks of her high school crush, and Jim, the "normal" one who is the high school crush of Laura and whose high school glory amounts to nothing in the present time. The characters are unique, but their struggles can part of our very own lives.
Hence, the ethos of the play brings through the credibility and talent of the dramatist. We can certainly ascertain that the classic quality of The Glass Menagerie proves the successful ethos of Tennessee Williams.