The only "tool" that I know of for adjusting the cap is used for the plastic snap caps on some rollerball and fountain pens. One example is this one from Craft supply
It is not the one you are thinking. I looked at that one first. The piece I have is .430 outside diameter, .369 internal, and diameter.786" in length. It is made from steel.
That is used on the long clicker to press the upper click mechanism in place without damageing it. Press in the nib section first then when pressing the upper section in place place this between the press and the clicker and press down on this. Which in turns presses the clicker in place in the brass tube.