Well, spent a heck of a lot of time making this today. It doesn't look like it would take time, but I couldn't figure out how to make a shallow taper on my lathe. No matter what I tried, something was fouling somewhere.
I ended up making steps like a staircase by eye and blending them together with a file to taper from 4mm to 7mm. That 4mm neck makes things hard, can't put much pressure on the tool, or a file. The pressure from the live center distorted the end, had to lightly use a file to touch up that end, as it was catching on the ID of the o-ring. There's a step at the start of the taper, it's small now and I can get the o-ring over it, which is what counts. The only file that seemed to have a decent metal removal rate was my lathe file, the other smaller ones just weren't cutting the same. But the lathe file was kind of big relative to the piece, so it was a little awkward.
One thing I didn't think through in the heat of the moment. I drilled a 1.95mm hole for a press fit pin in the 3/8" stock, but neglected to press in the 2mm pin, while it was easier to handle. Now I need to compare the holding power of an ER40 collet on a 7mm piece to the force of pressing in a 2mm interference fit pin. Oops. Work piece is 70mm long total. There was about 12mm in the collet, give or take when this picture was taken. I might shorten the piece once I've tried it since that 4mm section is just waiting to get me in trouble.
Strangely, cutting in reverse seemed to work better with less chatter. The tool had more stick out than usual, due to the presence of the live center. Used a RH insert and set my lathe to feed towards the tail stock, while the chuck was rotating in the forward direction. So I set my ELS to "left hand" feed.
Need to insert the pin somehow, and make a corresponding looser fitting hole on the probe. Fortunately I can modify the probe easily and safely, as the high pressure section is relatively far from the end.