The S-meter's zero setting can be affected by more than one kind of drift.
To start, cleaning the zero-adjust pot in the rear will help if that's part of the problem. All rotary controls become noisy eventually. A proper 'control cleaner' is best for controls that get cranked up and down regularly. But considering how seldom the S-meter zero should get turned, a simple non-residue contact cleaner is probably okay to use. The light lube contained in a proper "control cleaner" is there to reduce friction damage to the sliding surfaces inside a rotary control. That 'zero' pot shouldn't get turned all that often. A non-residue cleaner shouldn't shorten its life the way it would for the volume control. That one gets cranked a lot more often than the S-meter zero.
The far-left (as seen from the front) 6BA6 tube is what controls the meter. Any oxidation in the tube socket or on the pins of the tube will be trouble. Always a good idea to make sure no parts attached to that tube's socket look overheated. A bad tube could have damaged a resistor years ago. And if the color bands all look fairly bright, that resistor probably has not been overheated. Not a big risk, but always worth a look anywhere in the radio, and not just under that tube socket.
We find that simply 'rocking' each tube in its socket while listening to a steady signal will reveal noise from dirty or oxidized surfaces in that socket or on the pins of that tube. We use CRC brand "QD" spray cleaner, directed at the tube's pins with the tube cocked slightly to one side in the socket. The tube gets 'rocked' around in the socket to scrub the contact surfaces. Once that tube remains quiet while it is 'rocked' we move on to the next.
We also "tap" the side of a tube once the socket is quieted down just to be sure there are no structure issues inside that tube. A tube (in a clean socket) that goes "crackle" when tapped on the side has a problem and will prevent the receiver from being stable.
The two tiny metal 'Nuvistor' tubes V1 and V2 can be stubborn about quieting down and might require repeated application of the cleaner.
But any kind of shift or drift in the behavior of all the radio's circuits can have an effect on the S-meter.
73