This is very likely.

The switches are making a connection between a row and column that is decoded.

Interconnections are very expensive, thus the desire to reduce their size by scanning.

Even most push button phones do this.

Three columns, four rows.
Only seven connections to decode 12 buttons.

I pulled apart the two layers of the membrane and traced everything out. I thought once again I was on the right track, but it looks like some buttons are using 4 wires instead of my original thinking of three. One lead appears to go all the way through every button, so I'm thinking it's a ground or some sort of common. I can get some of the buttons to work (start and stop) but when I start adding things like ramp up and down it causes problems. Like if I add ramp up, my start and stop buttons will no longer work. It's extremely frustrating.
There has to be a way and I need to find it. I pretty much have to now since I tore apart the two layers. I've heard of other people replacing them with push buttons, of course they didn't go into detail as to how they figured it all out.

4 leads are scan-out and 4 leads are scan-in - that will give you up to 16 identifiable switch combinations.

You would need to use an oscilloscope to identify the scan-out leads and then identify which switch sends the pulse train back to which input.

While you can replace the membrane switches with other momentary contacts switches, what's the point? You still need the micro-controller to interrupt the input and produce the desired result and output.

Unfortunately, taking apart most membrane switch circuit boards and reassembling them, greatly reduces their reliability.

Can't you just relabel them?

As far as the three leads, I think it's just coincidence you're getting a response. While it could be some sort of very unusual switch matrix, it's really quite doubtful.

How!? That's exactly what I'm trying to do is just replace them with simple normally open, momentary contact, push buttons.
I have the controller. It's pretty small and I'm going to put it inside of an enclosure, on the outside of the enclosure I will have my new push buttons to do the various functions. This is all mounted to a pendant arm on the lathe that I can reposition to be out of the way as needed when working on turnings.
As to what the point is, the treadmill console board was rather large and ugly. I don't need nor want a huge plastic board just to do basic functions. Plus I'm going to be eliminating some of the functions too, like the workout routines, calories burned, etc...

I took another look at it tonight. I have the two "sides". One side has three pins that go into a ribbon, the other 5, so two ribbons total of 8 pins, wires, leads, whatever you want to call them. On the side with only 3 pins it appears that it goes from one of pins, through all of the function buttons, and then out another pin. That makes absolutely no sense to me though how that would work. If two pins are basically one, why even have the second? Is it feeding something (voltage? ground?) through all the function keys and than back into the board?

I'll trod back into the shop and try to make sense of it. It seems so simple yet so difficult. I was expecting to be able to just trace everything out, find the two leads I would need and bam be done with it...

The scanner logic is pretty simple.
It drives one line at a time and looks to see if any connection has been made by a switch.
It knows what line it is driving, and what line is now connected to that line.
That allows it to determine what switch is closed.

You might be able to play around and figure it out, but an oscilloscope would make it a lot easier to identify the output lines from the keypad decoder and the input line back to the decoder.

I have had to design circuits to do this every few years for different applications.

Hopefully no one used any of the common tricks to further reduce the interconnections.

using my meter to test continuity I traced pin 1 along the board. Half way through one of the buttons I lost tone (it was reading something like 25 ohms).
I kept the one lead on the button and moved the other from pin 1 to pin 8 and I got tone again. Can anyone explain that? From what I think is going on, pin 1 and pin 8 are virtually the same (electrically speaking they follow the exact same trace) but it's like it has too much resistance or something and can't make it all the way through the board or something so pin 1 stops half way through one of the buttons and pin 8 takes over and finishes.

I have no clue, I feel like I'm loosing my mind and grasping at straws. I've got to get something figured though and get my shop back up and running.

As for figuring out what is rows and what are columns, I think I can very easily. Overlaying the two membranes on each other I can see the grid very clearly. But it still doesn't make sense to me that I need to touch three leads together to get a function and not just two. I know it's not just a coincidence either. I get NOTHING with just two leads touching. Of course this frustrates me to no end though because I feel so close yet so far away. I'd have to double up wires on one side of a push button, but of course doing that causes problems the more and more buttons I add because more and more wires get connected together and act as one. So SOMEHOW I need to come up with a button that will momentarily close three connections and open all three when the button is released.

It is a 3-pole single throw switch. Often abbreviated to 3PST or 3P1T.

You could also use a 3 pole double throw switch (3PDT or 3P2T) and simply not connect the second position contacts.

Higher resistance sort of goes along with flex membranes.
While rigid printed circuit boards are very low resistance since copper foil is present, the flex membranes cannot use as solid and thick of a conductor.

Double feeding is not uncommon to keep the resistance low enough for operation at low logic voltages.
The input impedance of the chips can be very high, so not a lot of current is required.

Some membrane switches do not even use DC voltage.
They sense the coupling produced with an AC wave through a finger that is near the two (or more) lines.

A single exciting line may be used for all the switch positions, while the other two 'contacts' are to sense the capacitive coupling at each position that indicates the button has been 'pushed.'

You have ZERO hcance of figuing it out with a simple continuity beeper.

He recommended I get double pole single throw (DPST) buttons. The ones I've found are pretty pricey though considering I need so many. I'll look into what you suggested, Brick. I don't want to fork out $35+ per button.

Thanks for all the help!!!

Save your money until you know for certain - if capacitive switches, you can not replace them with momentary contact switches.

The only way to know for sure is to reconnect the switch panel and use an oscilloscope to see what the signals are on each lead of the ribbon connector. Then analyze what pressing each key does.

It's also not a good idea to troubleshoot these I/O ports with a multimeter, especially with a continuity tester, as they can easily do damage to the ICs.

You might be able to use simple switches depending on how the capacitance is being sensed, but for at least some designs an actual switch will not work.

DPST buttons are not very common and will likely cost more than DPDT buttons.

DPDT are a pretty common switch.

ALCO switches (now TE Connectivity) are very good.

Switches have never been inexpensive, with push buttons higher than toggle switches.

Using two N.O. SPST momentary contact push buttons I have it working. Just like I said from the start, I have to close three contacts instead of two to get a function to work. I just wanted to let you know because there seemed to be some confusion in that, that couldn't be the case.

So I have some DPST buttons on order, but for now I'm using two SPST buttons and have to press both buttons down to get a function to work. It's jerry rigged a little (for now), but at least I can turn projects until my new buttons get here and I can wire them in permanently.

$50 (for the treadmill off craigslist) variable speed lathe conversion. Not bad considering the factory wanted $800 for a conversion kit.

And an actual DC motor with a speed control (usually just a dial) from a motor surplus place might have been even cheaper (and would have consumed less time).