1999 Buick Century Odometer

I concur with @JosephEMeehan that there’s a significant probability from the symptoms reported this is just a loose or oxidized connector. If fixing it requires removing the console, it will still be expensive at the mechanic’s hourly rate charge, but at least if it’s just a connector problem, it won’t require finding/ buying the whole replacement console.

As some perspective, the clock display on my car went ker-poof about 3 weeks after the 3-year “bumper-to-bumper” warranty expired, and for the past 17 years I’ve lived with it and haven’t suffered much. If reaching up and jiggling the connector doesn’t fix the problem for the OP’er, maybe living with this problem is the best solution.