Hello,
Thanks for the video. I gives a fair idea of where to look. I can see that your are using the orthographic projection. Does it also happen in perspective mode?

@Scrubs
Interesting question, actually. I tried zooming in again in Perspective Mode and interestingly the gizmo didn't behave weird. In fact, I tried switching between orthographic and perspective mode: when zooming in on a single part in perspective view, at some point the gizmo will disappear because the camera is too close to it (clipping); if I switch back to orthographic view, the weird behaviour of the gizmo will start at that exact point, behaving more and more weird when I continue to zoom in. So I guess there is a parallel there somewhere. I also noticed that the problem occurs the faster the further the part is located from the origin (camera rotates around scene origin), with gizmos of objects close to the origin disbehaving not as much or not at all. When moving parts with disbehaving gizmos to the center, the disbehaving will reduce or discontinue.

I'm not a coder, but to me, it seems like scaling a part down in Blender too much to a point where it will grow again, but inverted; something similar happens visually with the gizmo when I zoom in to much. I think this might be produced by the camera rotating around the scene origin, thus the further objects are located from it, the sooner the camera would clip a gizmo in perspective mode, then making the orthographic view gizmo disbehave. Just an idea, of course.

Edit: I tried rotating a part with the weirdly rotated zoomed-in gizmo: although the gizmo is visually badly rotated, the translation is the same as for the zoomed-out gizmo (right angle X/Y/Z), so it actually seems to be a visual glitch only.

Edit 2: if the glitch is actually a camera clipping issue, I guess the easiest way to fix it would be to make the camera rotate around the selection always, thus having the object in focus within the clipping bounds perfectly all the time. Or adding a clipping option or something (if it actually is dependend on clipping, of course).

It's all good. No relation with camera clipping. It is only an issue with misbehaving control planes for the gizmo - it would be a bit long to explain.
I will check that when I will finish what I am currently working on.