Singing duets is brilliant! All the fun of a solo and half the stress as there is somebody else up there to share it.
But those "what to do" moments can be hard...here are a few tips I have picked up over the years...
First, make sure you know what to do during the song - choreograph it. If you don't do this there is a risk that one person will make a lunge for the other's hand just as they decide to wave their arms about. Then practice those moves so that they look natural (nothing worse than the "here comes verse 2 - now we switch to position #3" syndrome).
The ideal is to practice with your duet partner in front of somebody who can advise on what it looks like from the front. Failing that you can use a mirror and/or a willing substitute (family member??)
Don't look directly at your partner while you are actually singing - not only because it can be distracting but because - unless you are amplified - the sound will go to him and not to the audience. Generally if you are three-quarters on it will look from the audience's point of view like you are in contact with each other but they will get the sound.
(This explains the popularity of the "man stands behind woman with his arms around her" position in Am-Dram. Both parties can face front while at the same time looking romantically involved with each other. And less chance of the giggles).
You can, however, look at your partner while he is singing and you are not. This helps to focus the attention on him.
The key when you are not singing (and indeed when you are) is body language. You don't need to do much if what you do is right. And you don't want to do much, because the focus should be on your partner at that point.
Depending on where you are, you can just look at him with a happy expression (if that is appropriate to the words of the song), which will help focus the audience on him too. Note that "happy expression" does not mean a big grin
! Think about what your eyes do when you are happy - they light up and that lifts the face. Try it in the mirror - see the difference between the "fixed grin" effect when your mouth leads the expression and what it looks like when it comes from the eyes.
If he has his arms about you at that point you can lean into him - even close your eyes. In general less is more. You hardly need move at all, and it won't look like you are frozen - as long your body language is appropriate.
Remember also that your personal perception of time will be totally different from that of the audience. Your reactions are speeded up so it feels as if you are stuck for about 3 months while he sings his 16 bars. The audience, however, will be listening to the song and (apart from your Mum
) they will all be watching the person who is actually making the noise.
It may help you to look at other performances of duets (not only of this particular one) - see how the parties fill up the time and how they create an impression. You may also find it useful to read something about body language. Even (or especially) the "pop psychology" ones because in your case it is useful to pick up on the cliched stereotypical things that are a shorthand for "this person is happy/sad/angry/in love" and which an audience will interpret as such.
All the best - it's a gorgeous duet so just enjoy it!
Oops sorry - long post!