Why is my 2002 buick park avenue egr monitor not reading?

Is your Buick setting any diagnostic trouble codes or pending codes? If not, it's all about having the proper conditions met for setting the monitors. There are specific things the engine's processor is looking for, and apparently even in 1,000 miles and more, you haven't satisfied that criteria. Here's an article that may be able to help: https://repairpal.com/drive-cycle-issues PS - a good technician local to you will be successful in setting those monitors, or tell you what's wrong if it will not set. I know from personal experience -- I get monitors set 100% of the time, personally. It takes patience and understanding and experience. Or it just takes a ton of varied driving. Good luck.