Yes, the PMDX-126 supports normally closed switches in series. See figure 3 on page 21 of the PMDX-126 manual.
Can you give us more details about "doesn't work"? Does the LED for pin 13 or 15 turn on and off as the switch opens and closes (or vice verse, see below)? Have you tried the switches (and wires) from pin 13 on the (working) pin 12 input? Do they work there?
For example, according to section 6.1 of the manual, if you connect the switches between the "Pin 13" terminal and one of the "GND" terminals (on J11 or J12, not any other "ground" on the board), the LED next to the "Pin 13" terminal should turn on. When you press one of the switches (to open the switch contacts) the LED should turn off. Do you see that? If so, continue below. If not, that is a problem. Replace the switches with a short piece of wire. Does connecting the "Pin 13" terminal to GND make the LED turn on? And double-check your screw terminal connections. Some of the PMDX boards use "rising elevator" screw clamps, and if you put the wire UNDER the movable part and try to force it down onto the wire (turning the screw CCW looking down onto ti) it doesn't always make a good connection.
You don't say whether you are running Mach3 or Mach4 (or some other software). And if Mach4, which motion plug-in you are using.
In Mach3, click on the "Diagnostics" tab across the top of the window. Look for "Port 1 Pins Current State" near the right edge. Pin 13 is the 5th from the left in the top row, and pin 15 is the 4th from the left in the top row. Do these indicators turn on and off as you open and close a switch? This diagnostic does not rely on any signal mapping in Mach3. It shows the raw parallel port signals.
In Mach4, it depends what your motion controller is.