First a definition: a trackstick is also called trackpoint, pointing stick, or "that red knob between G, H, and B". I'll be using trackstick here, because why not.
This post is the continuation of libinput and the Lenovo T450 and T460 series touchpads where we focused on a stalling pointer when moving the finger really slowly. Turns out the T460s at least, possibly others in the *60 series have another bug that caused a behaviour that is much worse but we didn't notice for ages as we were focusing on the high-precision cursor movement. Specifically, the pointer would just randomly stop moving for a short while (spoiler alert: 300ms), regardless of the movement speed.
libinput has built-in palm detection and one of the things it does is to disable the touchpad when the trackstick is in use. It's not uncommon to rest the hand near or on the touchpad while using the trackstick and any detected touch would cause interference with the pointer motion. So events from the touchpad are ignored whenever the trackpoint sends events. 
On (some of) the T460s the trackpoint sends spurious events. In the recording I have we have random events at 9s, then again 3.5s later, then 14s later, then 2s later, etc. Each time, our palm detection could would assume the trackpoint was in use and disable the touchpad for 300ms. If you were using the touchpad while this was happening, the touchpad would suddenly stop moving for 300ms and then continue as normal. Depending on how often these spurious events come in and the user's current caffeination state, this was somewhere between odd, annoying and infuriating.
The good news is: this is fixed in libinput now. libinput 1.5 and the upcoming 1.4.3 releases will have a fix that ignores these spurious events and makes the touchpad stalls a footnote of history. Hooray.
 we still allow touchpad physical button presses, and trackpoint button clicks won't disable the touchpad