Welcome aboard, SupremeOverdrive.

The LED buttons that came with the board have 3 tabs:
-- LED
-- NO (normally open)
-- COM (common) -- shared by the LED and switch
The other buttons have 5 tabs.
- 3 tabs on the microswitch:
-- NC (normally closed) -- not used
-- NO (normally open)
-- COM (common)
- 2 "stirrup" tabs:
-- LED +
-- LED -
What to do?
1. (optional but
highly recommended) Verify that the LED holder (left-most red item in pic below) is installed in the same orientation in all your buttons.
Set your multimeter to diode check -- the LED will light dimly when the red lead is on LED+ and the black lead is on LED-.
The memory trick I use is black meter lead ==> stirrup next to the black tab holding the microswitch ==> LED- since black is usually ground for DC wiring.

2. Figure out which wires on the 3-wire are COM and NO. (touching them together = a button press)
3. Figure out which of those wires is COM by lighting a LED.
IIRC the ZD encoder is an active-high device, so:
-- The 3-wire COM wire should connect to the LED+ stirrup.
-- The 3-wire LED wire should connect to the LED- stirrup.
If your encoder isn't an active-high device, swap LED+ and LED-.
4. Hook everything up including a splitter for the 3-wire COM wire.
Instead of cutting/soldering the wires, consider using Quick Disconnect (QD) crimps.
The stirrups need 1/4" (0.250") QDs and microswitches _usually_ need 0.187" QDs.
Scott