Essentially, I'm trying to find an example of a function that is continuous but not uniformly continuous on $\text{GL}(2,\Bbb{C})$. I'm aware that this group is isomorphic (up to constant multiples) to the Möbius transformations. So I'm having a go at developing some geometric intuition there. However, as my prior inquiries indicate, my epsilon-delta skills are lacking. Hence, I find these sorts of examples tough to fabricate.
Edit: Norm is the boring Euclidean one on $\Bbb{C}^4$.