My spouse, ever the optimist, thinks that we can somehow get the university at which I am completing my graduate work to hire me as a spousal hire. Should my spouse mention this to her departmental chair (different department than mine)? And when should she do this?
First, let me say that I am shocked that no one had grabbed the "Chewbacca" moniker until now.
Universities in remote places have spousal hiring policies for recruitment and retention purposes. If your spouse continues to be a valued member of the Faculty
and is willing to credibly state that she will have to leave if you can't find employment, then the spousal hire policies should apply to you. In theory, your university should be as least as interested in offering a spousal hire to keep someone who has proven herself as to hire a promising candidate fresh out of graduate school.
But that's just the theory. Not all administrators may see it that way. Even if central administration would be whipping out their matching funds in a hearbeat if you both were new hires, the fact that your spouse is a bird in hand and you're an alum-to-be may make them hesitate. And if no one believes that she would actually apply elsewhere if you don't find work, it will be a non-starter. Ditto if your department would never hire one of its own even at a bargain price.
Assuming the threat of moving on is a credible one, then I have to believe it's better to say something sooner rather than later, to allow as much time as possible for good things to happen. The proper way to start the conversation would be for your spouse to bring it up to her Chair as an issue that affects her long-term plans.
The back-up plan: If no one seems interested in finding a spousal placement for you, either you or your spouse may need an offer from elsewhere to gain leverage.
Warning: This is just based on my impressions of how things have worked with spousal hires I've seen on steering committees. From my ass to your ear ....