@Monty - - At the risk of not being very helpful I'll offer the following comments, far from a positive identification - - -
It is unusual to see a slimline with a click mechanism.
Based on my experience it would seem to be a "generic" slimline from an "unbranded" source (not Berea, not Dayacom, etc.)
Whatever kit it is, it would seem to be a single-barrel modification of such a "generic" slimline.
The design of the clip seems to be the most distinctive feature in the picture you show. I've found 3 such offerings :
1) The styling of the clip matches the clip in the "Upscaled Slimline Twist Pen Kit" from WoodNWhimsies here :
A Slimline with an upgrade. Has a fancier center band and clip.
www.woodnwhimsies.com
2) As I said, it is unusual to see a slimline pen kit with a click mechanism.
But, It looks very similar to the PSI pencil kit shown here :
We created out Funline Slimline kits with economy and fun in mind and they've quickly become a customer favorite. In fact, they are so popular that we now have a Pencil version of the Funline Slimline Kit. Includes attractive ball clip and oriental style band and .7mm lead.Note: Our lifetime warrant
www.pennstateind.com
3) One of my early purchases of a slimline kit was from my local toolstore called KMSTools. . They show this pic (twist not click):
Creating unique, eye-catching pens with your wood lathe is fun and rewarding—and getting started is easy. At KMS Tools, we've got everything you need to craft one-of-a-kind pens that make memorable gifts and treasured keepsakes. This Slimline twist-
www.kmstools.com