Please could you clarify the purpose of your thread .......
Tell me if I have the right idea ....
You are showing, in your sketch, the barrel of the pen. .
At the left end you show the threads which accept the screwed on cap when storing the pen.
At the right end you show a taper which accepts the posted cap while you are writing.
Is that the essence of it ? . Are you trying to show how to get the correct sizing of the taper ?
If so, I guess that's why you say "Turn 1" tenon same diameter as threads"