We recently added one to the Green Tree Monitor enclosure & it's been an amazing experience. I've learned more about her behavior in a couple weeks spying while at work than months of standing in front of them.
The purchase was triggered by a bad experience with the male eating her eggs & her...
For our pair of Veild's I built their cage as a single unit 52" x 40" x 20" with 2 doors & a removable divider made of 1/4" wood sealed with linseed oil, covered with nylon screen to make it easy to climb. It has worked extremely well but they did seem aware of each others presence when it came...
Our male gets very uncomfortable, changing his patterns / movements & goes off feed while in shed. The female doesn't change her behavior at all.
The fact that he is still eating is a great sign.