Can an AMT service a wet compass?
Check 65.81(a). A certified mechanic can't perform any repairs or alterations on instruments. So legally you can't service a compass and return it to service as an A&P.
Service"? Yes! Repair, absolutely not...
In Canada, you can. As long as you have the manufacturer's manual and the procedures do not require specialized equipment, you can repair. Same with servicing.
A compass is considered an aircraft instrument by the FAA. Part 65 prohibits FAA mechanics from performing any maintenance including servicing on any instruments including compasses. The only procedure a FAA mechanic can perform on a compass is a compass swing and update the compass card, which is a required placard.