The problem arises from a dirty SSB fine tune control and can be fixed (if the control is not too damaged from age and wear) by cleaning the fine tune control with a good quality contact/potentiometer spray cleaner WITH a lubricating formula. The lube will keep the control turning smoothly and reduce contact wiper wear on the carbon track. Poor quality cleaners (like from Radio Shack) may only last a few days to a couple of weeks until the problem returns).

The problem arises from a dirty SSB fine tune control and can be fixed (if the control is not too damaged from age and wear) by cleaning the fine tune control with a good quality contact/potentiometer spray cleaner WITH a lubricating formula. The lube will keep the control turning smoothly and reduce contact wiper wear on the carbon track. Poor quality cleaners (like from Radio Shack) may only last a few days to a couple of weeks until the problem returns).
After removing the 5 screws holding the back cover on, gently lift the dual circuit board assembly out of the radio.
Spray some cleaner into the control via the underside of the control knob, then rotate the control a dozen times throughout its range, then give it another shot of cleaner and more excersise. This should be enough cleaning to solve the problem of warbling caused by a dirty fine tune control.
And while you are at it, give each slide switch a short shot of cleaner with a half dozen throws of the switch, then another quick shot of cleaner. Also, spray the volume and attenuator controls as well and a quick shot into all jacks whether they are used or not.
If the fine tune control is damaged by dirt or wear beyond cleaning, a new control is available through Sony Parts at a cost of $20 + (see a previous post on this group about the replacement).
The whole process should take about 15 minuets and the clock will have to be reset but preset memories will remain useable. And don't be stingy with the spray cleaner quality - the better the quality, the longer
the repair will last.
By the way, this problem/cleaning can be used on all versions of the 7600 line of radios.

the importance of a good quality cleaner with lubricant. DeoxIT is harmless to the carbon path, meaning it won't dissolve the pot's "innards" like some other solvents and it has a viscous lubricant that helps both protect the pot from accumulating more dust, dirt and corrosion and restores the smooth solid feel it had when new. I've used it for years on pots in vintage guitars and other instruments and it even makes wire-wound rheostats feel less crunchy and ugly. Regardless of whether you use that specific product, it pays to look for a cleaner with the same kind of attributes. There's no more rotten feeling than to hose out a potentiometer with some cheap crap and find out you've wasted it or in the case of the SSB synch pot on the 7600GR, losing the viscous lubricant can make the pot feel loose and actually create more of the warble you were trying to fix.