Pull the compass and send it to Viking, the company in the Tempest link. You probably need a new dome rather than just a cleaning - they discolor, plus they will put in an LED light, fill it with oil, and generally get it to good operating condition. Other reconditioners can do the same. It just didn't seem like a good DIY project to me.
When I loosened the wrong screws on my Ritchie compass and accidentally drained the oil, I just brought it to the repair guy to fix rather than do it myself. The trick to refilling it, so I'm told, is to put the oil in freezer to increase the viscosity and make it easier to refill. The glass dome can likely be replaced, if they still make them. They tend to develop spider cracks and discolor as they age.