Controlling 10-pin 2-digit 7-segment Display with shift register.

Howdy, I'm stumped and have a question like the original post in this thread. I've succeeded in working with a 2-digit 7-segment display (10 pin. stats here: http://www.xlitx.com/datasheet/CL3621AH.pdf ) The circuit and code are shown below to hopefully help someone in their journey.

Now, here's my thing. I intend to make a clock which shows Hours: Minutes: Seconds. Three blocks of 2-digit 7-segment displays. Obviously I need to chain latch shift registers like 74HC595, right? I'm familiar with that from other binary LED projects (through-hole LEDs, not components like this one.) Not familiar with the MAX2719 (7219?). But, sticking with the 74HC595 for now, I arrive at two questions:
(1) Do I really need 2 shift registers for this component? One per digit?
(2) I cannot figure out how to wire up two 74HC595s to this 10-pin component; any advice?

/*
    CL3621AH 2-digit 7-segment display
    http://www.xlitx.com/datasheet/CL3621AH.pdf

    ******* COMMON CATHODE **********

    connect ardruino pins 10, 11 to resistors (330 ohm) and
    then to component pins 5, 10. The rest connect direct.

    compenent      arduino uno
   ---pins-------------pins---
    5        dig.1          10
    10       dig.2          11
    __________________________
    3          A             2
    9          B             3
    8          C             4
    6          D             5
    7          E             6
    4          F             7
    1          G             8
    2          DP            9
   ____________________________

      Component pins (1 - 10)

      (10)     (9)     (8)     (7)     (6)
        |       |       |       |       |
  *******************************************
  *                                         *
         A A A A             A A A A
        F        B          F        B
        F        B          F        B
        F        B          F        B
         G G G G             G G G G
        E        C          E        C
        E        C          E        C
        E        C          E        C
         D D D D   DP        D D D D   DP
  *                                         *
  *                                         *
  *******************************************
       |       |       |       |       |
      (1)     (2)     (3)     (4)     (5)


   array digit[] values represent LED on/off switches

   0b[G][F][E][D][C][B][A]

  0b0111111, // Zero
  0b0000110, // One
  0b1011011, // Two
  0b1001111, // Three
  0b1100110, // Four
  0b1101101, // Five
  0b1111101, // Six
  0b0000111, // Seven
  0b1111111, // Eight
  0b1100111  // Nine

  ***************************************************
  This code just cycles through 00-59.
  ***************************************************

*/

// these values turn segments on/off to display
// representations of numbers Zero through Nine.
int digit[] =
{
  0b0111111, // Zero
  0b0000110, // One
  0b1011011, // Two
  0b1001111, // Three
  0b1100110, // Four
  0b1101101, // Five
  0b1111101, // Six
  0b0000111, // Seven
  0b1111111, // Eight
  0b1100111  // Nine
};

// declare digit 1; digit 2
int d1, d2;

void setup()
{
  for (int i = 2; i < 12; i++)
  { // we are using arduino pins 2-11
    pinMode(i, OUTPUT);
  }
}

void loop() {
  for (int j = 0; j <= 59; j++)
  { // first loop: 0-59 with some binary conversions
    d2 = j / 10; 
    d1 = j % 10; 

    setBrightness(10, 25);
    digitalWrite(10, LOW);  // LOW = active
    digitalWrite(11, HIGH); // HIGH = inactive
    shiz(d1);                // ones digit
    delay(10);

    setBrightness(11, 25);
    digitalWrite(10, HIGH); // HIGH = inactive
    digitalWrite(11, LOW);  // LOW = active
    shiz(d2);                // tens digit
    delay(10);
  }
}

void shiz(int n) {
  for (int i = 2; i < 9; i++)
  {
    digitalWrite(i, bitRead(digit[n], i - 2));
  }
}
void setBrightness(int p, int v) {
  // p = pin; v = value
  // common cathode, so high is low, flip the value
  v = 255 - v;
  analogWrite(p, v);

The following image represents my confusion. :slight_smile: