Without supercap the meter should work just fine.
If you remove CR17 & CR18 (dual diode) it is clear that when using battery power (9V) the clock should remain its values (not tested since I do not have a working 28x).
However when 9V removed and supercap removed the clock settings are reset to the beginning of time.
The reason to remove the rusty supercap is to eliminate a possible short on the supercap.
Since we are not at this specific meter we are unable to judge (even if it is possible) to see if it is the supercap.
Furthermore, since it is corroded it is best that after the unit starts working it gets replaced by a proper replacement (Panasonic of some sort).
It is true however that I have not seen many repairs (0) where such problems are solved. 9 out of 10 it is an FET which is broken (see other topics). However this issue blinking LED is never solved and I spent many hours searching online. This is the reason why I am trying to figure the thing out myself.
Thank you ElecSeb for great tips. I'll be on vacations too in couple of days. Will get back to this on return. However, I couldn't locate the NXP chip. Is it one of those on the other side of the board?
Correct, the square black BGA chip U26 (this is the heart of the 28x and e.g. controls your LCD), the MSP430 U13 (seems to do all measurements like in all other fluke products), they are talking to each other through a bus (not yet found/defined). The MSP has special JTAG higher frequency and needs to be programmed with appropriate programmer and the NXP is normal JTAG.