I don't think you can work with the EEPROM in-circuit as you get bus contention with the DMM IC. TL866 fighting with the DMM IC probably.
I solder-wicked and then lifted up the two 24C02 EEPROM legs SDA SCL and tack-soldered tiny wires, along with GND (3 wires total) and ran them to a programmer.
Used Arduino sketch with 3V level-translator (resistors/diode clamp) to read/write the EEPROM. #define DEVADDR 0x50 // I2C device address of 24C02 EEPROM
DMM write-protect WP jumper JP2 must be in to allow EEPROM writes. Using DMM 3V power on to run the EEPROM. DMM will give "Err03" I think if it can't see EEPROM.
This is my EEPROM contents with temp. function added. Yours will differ due to CAL coefficients. Do not overwrite yours.
So read your EEPROM, save that then edit the two bytes to allow temperature.
Attached .HEX file is from Russian forums on kazus.ru; Has 600V alarm voltage instead of 750V I think, and no temperature enabled.
You can change auto-power off time, backlight timer, LCD contrast, alarm voltages etc.
Many people changing EEPROM contents on DMM's using the same IC like ZT101, ZT102, AN8001, AN8002, HP-890CN, HP-770HC, UT139C etc.
0 1 2 3 4 5 6 7 8 9 A B C D E F
00: FF FF FF FF FF FF FF FF FF 52 00 FA 00 00 BE 03
10: 10 17 0F 27 52 03 6E 50 64 4B 3C 3C 0A FF 40 FF
20: 3C 98 81 81 64 00 96 00 00 80 8D 80 00 80 FE 69
30: 4E 02 09 9C FB 09 8C 01 0A 18 FC 09 36 FC 09 00
40: 00 01 00 01 00 07 98 00 64 00 64 00 64 00 00 00
50: 00 80 00 80 00 80 00 80 00 80 00 80 00 80 00 80
60: 7B 7E EE 7F 0A 00 99 2A 00 00 00 00 00 00 00 00
70: 8B 82 00 80 AC 82 E0 7C 18 01 00 00 00 00 00 00
80: 00 00 00 00 00 16 00 10 00 0C 00 07 13 01 12 03
90: 00 00 00 00 00 00 00 11 00 0D 00 09 15 02 00 04
A0: 00 00 00 00 00 00 00 00 00 00 00 0A 00 00 00 00
B0: 00 00 00 00 00 00 00 00 00 00 00 0B 00 00 00 00
C0: 0D 00 02 10 0D 00 03 20 20 00 03 20 20 00 03 10
D0: 1F 80 FF 7F 00 80 00 80 41 00 03 05 0D 00 02 20
E0: 00 80 00 80 00 80 00 80 00 80 00 80 00 80 00 80
F0: 0F 80 FF FF FF FF FF FF 5A C7 CC 0F 0F A2 00 00
Kerry Wong has some info on his site where he was into the EEPROM.