Hello Fid,
You are most likely correct about the Frazer.
Here are two photos taken from my two 1947 Kaiser Specials. One shows a bare, splined, push-on shifter lever (which takes a push-on end), and the other shows the shifter lever with the end already in place. The photo of the missing shifter lever is from a very late 1947 Kaiser Special, and the photo of the installed shifter end is from a very early 1947 Kaiser Special.
I need an end for the one missing on the later car. I am assuming that the lever on that car also required an internally splined or just round cross-section, push-on end.
Thanks for your input,
Jerry