The MysteryChip, seems to be an etched, and custom programmed Programmable Logic Array chip from Hitachi.
https://pdf1.alldatasheet.com/datasheet-pdf/v … HI/HG61H15.html

It could be emulating a wide variety of possible RTC chips. Which one? Beats me. Maybe these were cheaper than an RTC, or these are multifunction, containing the RTC and some scan/decode functions? Heck if I know.

Minus Zero Degrees has a small section of RTC chip programs. Might be worth a shot to just trial and error them, and hope one works.
https://www.minuszerodegrees.net/rtc/rtc.htm