Schuh -- One critical clue is if the hum is there when the selector switch is set to mono FM. In that mode, the multiplex circuits (that decode the stereo information) are completely removed from the audio path. If there is no hum in that mode, then service to the multiplex section is indicated. If the hum is still there, then it is originating in the FM tuner circuits. If that is the case, have the tubes carefully tested -- particularly for any heater/cathode shorts. Tubes in the tuner section with this condition would still allow the FM section to "work", but can induce an audible hum in the process.
When you test the tubes, note the socket they came from so that you can replace them in exactly the same socket they came from. This will help preserve the alignment of the tuner section.
There are other conditions that can cause FM tuner hum, but tubes with heater cathode shorts is one of the most common.
Good luck with it!
Dave