I decided I better check my wife's fob, since both were in the car when the low battery signal came on. With only my fob...no low battery alarm, but with only hers it did come on. I tested her battery and it was even better than mine, a full 3v. I didn't see any contact corrosion, but wiped them down and reinstalled the battery. Now no low battery signal. Hmmm...
I had a similar problem with the left rear tail light a year or so ago. It would not come on, although turn and reverse were OK. Of course, that is the built-in LED and the whole tail light has to be replaced, so I did that and it would not work, either! The dealer confirmed voltage was present on the plug, which is why he wanted to change the tail light, but what I finally discovered was the socket on the lamp had a "dirty" connection. Cleaning the female socket with a paper clip restored operation of the original lamp and I was able to return the replacement for a refund. I've not had a problem since.