Not sure what way you are reading the pins on the display.

Looking at the face of the display (glass tube) the plug that plugs into it is nombered right to left,  very left pin 21, very right pin 1.

So you should have 5 Volts AC between pins 13 and 3.  5 volts DC between pins 12 and 4.  These are pins of the plug not the display glass

Edit: wrong way around Very right pin is 1 and left is 21.. Have corrected in post above.