Clint, just take your time and pull the guts out of the speedometer housing. Use some brake clean spray spray and really give it a cleaning. Then use some light oil, like 3 in 1 or sewing machine oil, and give each joint a little dab. Brake clean shouldn't hurt the dial or odometer numbers, but check a small place first! WD40 is also a excellent cleaner and will oil at the same time. You really shouldn't have to take anything apart other then pulling the sheet metal case off.
Once its clean, run it with you drill motor and check it out.
Joe