That is odd, but that's life with human beings.

Without knowing the situation surrounding your wife's driving habits, I take the possibly outrageous liberty of making this suggestion:

1. Don't talk about it for a few weeks
2. Pull the light bulb (it's dead easy, instrument panel screws are behind little rectangular covers at bottom corners)
3. When she notices that it's "burned out", promise to fix it next time you get a chance to get to the dealer.
4. Hope that she stops missing it soon.

She might even enjoy shifting on her own schedule - isn't that why you have a "stick" in the first place?

If she catches on and the s*** hits the fan, you can tell her that you got the idea from some goof on the internet.

Or even worse....

Take the bulb out, blow it with house current, and replace it. Then you can show her that it really is burned out. Hope she doesn't ask you to "borrow" one from one of the idiot lights. Then she has outsmarted you, unless of course the arrow light is "special".