I saw this many, many moons ago on 60221. It was doing the same thing, only with the E-4 autopilot, and as well had been doing it for many years.
The fix was found to be the elevator trim tab actuators (jackscrews). The maintenance books say to ops check them you run them up and down. What they wern't saying (and was figured out by another crew chief, Tony Jeffrey) was there needs to be an air load applied to the trim tabs whiole running them. Do this by allpying a small amount of pressure to the tab just aft of where the actuator attaches to it while running the tabs. What you will most likley hear is a banging coming from inside the elevator, at the forward end of the actuator. This is the internals of the actuators slipping. The actuators have no time change (we asked for this several years ago, late 1980's), and are a real "mother" to remove. I'd recommend removing the elevator and soaking the bolts with penetrating oil. We did this on 60223 in around 2001 when the banging was discovered on it. After a week of "whenever anyone walks by, squirt oil on the bolts", it still took using a rivet gun and angled rivet set to remove the bolts, as they were siezed in the rod end that rotates. Also, keep in mind, that the trim tab cables used to be a 6000 time change, don't know if they still are, and are usually "forgotten" due to the fun of replacing them, so this would be a great time to replace them, too.
We asked for changes to the books several years ago, to add in the simulated air load and a time change for the actuators, but were ignored.