Going with voltages? Fair enough and it is low voltage DC (not like you are probing live mains voltage or worse). I normally do resistances but as a great man once said "first rule of troubleshooting is thou shall measure voltages" and it is not like the two concepts are unrelated.
6.4V is an odd one -- most logic levels are anything but that (see Logic-family switching levels, 5V or maybe just about 3.3V I would expect for stuff of that vintage, else a full 12 or 15 for some oddities) but without knowing otherwise I will accept it. Multimeters of that style (they occasionally have as slightly different shell but that is a fine example of the cheap and nasty multimeter that most people getting into this sort of thing get at first and ultimately regret later down the line when they have a go on something shinier) also have a very nasty habit of being that kind of out of range too, though in any case that stark a difference is enough to note in this.
A low voltage at a similar point would point to a high resistance somewhere along the path, one that would break a button functionality. For it to happen to multiple controllers in short enough a period (even more so as Z button failure is so very rare in general) does however cause me to think short circuit making something go pop where I would expect dry solder joints to be more of a various points over years, mechanical stress (which could be a controller but most things I see are worse than that still) and possibly temperature ranges (I often see it in car switches, which may also do high current in the case of electric windows).
At the same time looking at
https://upload.wikimedia.org/wikipedia/commons/7/7d/Nintendo-N64-Controller-Motherboard-Flat-Top.jpg I am seeing what looks like both corrosion and dry or maybe cold solder joints so maybe.
Simple switches work in one of two ways.
They either cause a voltage to be applied to a pin (pull up) or for the ground to be applied to a pin (pull down). This is why if you follow the circuit traces all the buttons will probably have a common point where they all join up on one side of the switches (do also be sure to measure both sides -- if geometry changes then you don't want to be measuring the wrong part of the switch, one of the reasons why resistance can be easier to do).
Looking at that image you might be able to short each side of the Z pins out (if you have the chip readable as in that image in front of you then by the copper triangle in the bottom right I am guessing is where the Z button board comes in and see if the system displays Z as being pressed. You may or may not want to use a fairly low value resistor here (carbon trace switches have a bit of their own resistance which has some effects in this sort of circuit, see floating voltages if you are curious, though for a short test a wire will probably be OK). In a strict test you would be desoldering one of the wires (in case the whole thing had shorted closed and in essence made the button think it was pressed the entire time*) but you might be able to skip that here.
*ever had to unplug and replug a controller because someone held the stick during startup? Same idea.