I just found a couple more Noble brand rotary encoders in stock. Out in the open, you can see a big clearance notch in the casting, for the element connections to the leads, and even see the wiper partly - there's plenty of opening to spray stuff in there. I think you'll find the same thing on yours if you remove them from the board, so cleaning them out and lubing should be easy. No need to take apart.

Ed

I've got the HP 54540C version here and it behaves the same as yours. I've had it about 9 years and it doesn't seem to gave got much worse although I hardly ever use it now. It generally seems worse just after starting and gets better. The horizontal control is worse than vertical.
The vertical typically gets it wrong maybe 1 in 5 but the horizontal control is worse. It is probably wrong 3 out of 5 when first started and then improves. I have done nothing about it and just accepted it. I replaced it with an HP 54825A scope a few years later.? The HP 54825A also suffers from this issue but not as much. It gets the direction wrong maybe 1 in 10 times on the CH1 vertical and on the horizontal control.

I always assumed this was done optically and was adjustable somewhere. Neither scope misbehaves badly enough to make me want to do anything about it. Both were salvaged from a skip/dumpster so I'm not that fussed about getting them to work perfectly.

The "circle with wiggle" mark is almost certainly Noble brand. These things are held together by the spread forks of the pot metal front shell at the corners of the back plate. With good flat-jawed pliers (preferably) or side wire flush-cutters, and careful working, you can grab each fork and compress the tines back together - try to go only just enough to release the back plate. Since the forks are pot metal, I'd say you have a 50-50 chance of successfully squeezing them just enough to get it open, then spreading them back out intact when finished - only one time. A second attempt will surely break the tines.

But, the good news is the simple structure can be easily epoxied back together, even if all the tines break off. The base of each fork should fit well into the corresponding notches in the back plate. Wash off any stray lube oil on the outside after all fixing is done, with IPA. A nice little dab of a quick-set (1-5 min) epoxy right on top of each fork, spreading slightly onto the back surface, should do it. Be sure the alignment is good, and squeeze the plate against the front casting until the epoxy sets up. If you do it right and quickly, the epoxy won't soak in too much, and will leave a glob that can be sliced off if necessary for future maintenance. If you manage to keep the tines intact and don't need epoxy, you can spread them back out carefully with needle-nose pliers, working against the back plate or casting features only for leverage - never the board or contact pin area.

If you need to find replacements or equivalents, you'll have to figure out the exact function of each unit - how many detents, resistance values, dimensions, etc. These may be standardized components with second-sourcing available, but you have to know what to look for. From the pictures, it looks like they are all pot elements with three leads. Next, is there a manual for this, showing the circuitry and values, and maybe the part numbers and such to cross reference? If these really are only pots with detents, then without any more info I'd guess the uP reads the pots with an ADC to know the setting. Are the settings absolute? IOW, if you turn it off, then change the pot setting, then back on, does it go to the new setting? There are specially patterned pot/encoders that provide pulse rotation and direction signals for up/down operation, but I don't recall if any can do that with only three leads*.? *(see below)

Lastly, was this model still made in the mid-1990s? If so, I'd think those "9" numbers are indeed date codes, while the dashed ones look more like part number details. Comparing your "1-2-36" codes to my Noble datasheet, I'd guess it means there is 1 circuit, 2 bits, and 36 "electrical positions." You can't tell the electrical easily from outside, but you can count the mechanical detents. From these numbers, I would guess that it is a relative (not absolute - not enough bits or leads), up/down counting wheel. So, if this is indeed the case, then it answers the question about having enough leads to work. If you take one of these apart at some point, you'll probably find two rotary patterns of 36 steps around, alternating open and conduction (the electrical positions), that are slightly out of phase (or the wipers are out of phase), or, maybe one pattern only, with some kind of wiper arrangement offset just right to get the alternation and phase. I think I'm remembering now - one lead is common, and the other two are resistance or conductor elements with alternating on/off states versus the common lead. The rotation is indicated by the state changes, while the direction is encoded in the relative phase. So there you go - three pins can do it. If this is actually the deal, then it's all digital, and no pot resistance measuring is needed.

One final, last thing. There is a way to get liquid cleaners and lubes into the pots, especially if you're removing them anyway. If you have some decent vacuum equipment, you can submerge the pots in a vacuum jar setup, then pump down a little and release so it will pull some inside. These are not sealed much, mostly against dirt only. All the joining surfaces and shaft holes through the front bushing and back plate, for instance, are wide open to getting liquids inside. Even without vacuum gear, just soaking them in the liquids overnight should get something in.

Ed