Password analysis
I found everything about these passwords on this Tama Zone thread by the user binary.
The passwords in the Jinsei series are 14 digits long.
There are eight variables: six of them have two digits, and two of them have one.
They are the following
- Current Tamagotchi's ID number [T1 & T2]
- Previous generation's ID number [G1 & G2]
- Current mail item ID number [N1 & N2]*
- Employment ID number [E1 & E2]
- Destination (Tamagotchi Town, Urarama Town, a special destination, etc.) [D1 & D2]*
- Session number (random) [S1 & S2]
- Pattern [P]
- Checksum [C]
*The four digits used in the login code for the destination ID number and the mail ID number are used in the logout code as the received item ID number. These are the four digits that appear before each item on the password generator in this order: D1 D2 N1 N2.
You may find the character's ID numbers in the Tamagotchi list.
I have not been able to gather all the letters' ID numbers yet… 
The session number is just a number randomly generated each time you get a login code.
Employments
| Number | Entama | Uratama |
|---|---|---|
| 01 | Scientist | Festival worker |
| 02 | News anchor | Comedian |
| 03 | Teacher | Circus performer |
| 04 | Doctor | Comic artist |
| 05 | Banker | Toy maker |
| 06 | Singer | Enka singer |
| 07 | Fashion designer | Band member |
| 08 | Baker | Jeweler |
| 09 | Hairstylist | Dancer |
| 10 | Florist | Magician |
| 11 | Hot springs attendant | Adventurer |
| 12 | Preschool teacher | Bodybuilder |
| 13 | Police officer | Fighter |
| 14 | Travel guide | Firefighter |
| 15 | Chef | Carpenter |
| 16 | Weather changer | Boat operator |
| 17 | Starting lights operator | Alarm clock |
| 18 | Living clock | Smile sign |
| 19 | Super Unchikun helper | Cheerleader |
| 20 | Royal servant | City lights operator |
| 21 | Preschool student | Preschool student |
| 22 | Intelligence student | Humor student |
| 23 | Style student | Gorgeous student |
| 24 | Kindness student | Passion student |
| 25 | Preschool candidate | Preschool candidate |
| 26 | Preschool graduate | Preschool graduate |
| 27 | Graduate | Graduate |
| 28 | Unemployed | Unemployed |
Destinations
| Number | Destination |
|---|---|
| 0X | Too young for preschool |
| 1X | Preschool student |
| 2X | Student |
| 3X | First day at work |
| 4X | Worker |
| 0Y | Mame City |
| 1Y | GuruGuru Town |
| 2Y | Patchi Forest |
| 3Y | Gozaru Village |
| 4Y | Berry Town |
| 5Y | Flower Hills |
| 6Y | Oyaji Village |
| 7Y | UFO |
The "X" will be either a 0 or a 1 on an Entama, or a 4 on an Uratama.
The numbers that end on "X" are for normal visits to Tamagotchi Town or Uratama Town.
The "Y" will be either a 2 or a 3 on an Entama, or a 5 on an Uratama.
If the number ends in "Y" that means you used a ticket or an UFO to go to one of the special locations.
Patterns
There are five different patterns. The pattern digit will always be the sixth one.
| P = 0 or 1 | ||||||
|---|---|---|---|---|---|---|
| D2 | G1 | S1 | E2 | S2 | P | G2 |
| C | D1 | T1 | E1 | N2 | T2 | N1 |
| P = 2 or 3 | ||||||
| E2 | D1 | D2 | S2 | T1 | P | S1 |
| C | N1 | T2 | G2 | E1 | G1 | N2 |
| P = 4 or 5 | ||||||
| S2 | T2 | E1 | N2 | C | P | G1 |
| N1 | E2 | S1 | D1 | D2 | T1 | G2 |
| P = 6 or 7 | ||||||
| S1 | N2 | N1 | T2 | G2 | P | T1 |
| E2 | S2 | G1 | E1 | C | D2 | D1 |
| P = 8 or 9 | ||||||
| G1 | C | N2 | S1 | N1 | P | E2 |
| E1 | D2 | G2 | D1 | T1 | S2 | T2 |
Checksum
This number must be the result of adding every other number together and taking the unit digit.
Example
0709475
1050204
- Tamagotchi: Tensaitchi [59]
- Previous generation: Pukatchi [54]
- News: Peaceful day [07]
- Profession: Scientist [01]
- Destination: Normal Tamagotchi Town visit as a worker [40]
- Session: 00
- Pattern: 7
- Checksum: 2 (5 + 9 + 5 + 4 + 0 + 7 + 0 + 1 + 4 + 0 + 0 + 0 + 7 = 4[2])
To generate a logout password we must replace the digits for the destination and the news for the ones we want. For example, if we want the Hatena dating card #3 [5187] we would get:
0789475
1050215
We can also change the pattern:
1510530
8894057