Wow you must be the only one in the world with another one! I thought I had the only one, from the info I've gathered the All-trac sedan was only made for one year in 1989, which is the same year as mine.
To answer your question, it depends on what type of transmission you have, if it's a manual, it's full time All wheel drive, and the center button will is only a "diff lock" button, meaning it transfers power 50% and 50% to the rear when locked. It looks like this:
If you have an automatic, then it uses a different system, where it is in 2wd untill you hit the button then it engages the AWD.
If the sound doesn't happen when you are going forward then I would it's something to do with the reverse. I wouldn't worry too much if it drives okay in 4wd in forward. Any pics of it? Here's mine:
