Thanks to Kalizweb I've been reading The Savant's Rantings, a blog with a lot of posts on Twilight: 2000. It's usually v2.2, which I own but I'm less familiar with than with v1.0, the T2K I played originally.
One of the posts I really liked was this one about initiative:
Take the Initiative - Twilight: 2000 Initiative Mechanics and Options
What's interesting about T2K, in its original and later incarnations, is that physical agility and movement speed aren't relevant in initiative. What is, is a mental readiness to act based on several in-game factors. In the original game, which forced you to skip turns based on your "Coolness Under Fire," you could act quickly but not often if you weren't elite or a veteran. In the later game, it's not exactly like that but your experience matters a lot.
It's an interesting concept to think of for a game - basing when you act on your experience and not your dexterity. The analysis in the blog post is worth the time to read if you are mucking about with initiative house rules in your own games.