Hello 2nOrderEDO:
I am repairing my HP8593A, still need some time to finish.
HP859x was built around 1990, it's been 30+ years, you may want to check:
1) NVRAM battery. Most likely it is dead. Mine measured 0.3V (should be 3V), therefore, all the correction constants data were lost. With an invalid NVRAM, the boot is not consistent. After the battery is changed to a new one, mine cannot boot. I have to discharge NVRMA, boot and connect the battery back to do calibrations. The battery TL-5104 life is 8 years at 25degree C, and 1 year at 50degree C, mines never changed since 1990. After 33 years, it finally died.
2) The EPROMs may be bad (some bit flipped). My HP8566B had that problem, after I copied that EPROM from a working unit, it was fixed. HP859x has 16 LEDs, the top 4 are for EPROMs U7, U6, U23, U24, if any one of them is bad, that LED will turn on. Just check that.
3) Power supply: some electrolyte caps ESR are too high, replace them.
4) The power supply PCB connector: a D-sub, some of the pins may not contact well. Over the time, it causes randomly power shutdown, unplug and plug back may help.
I hope this can help.
Lin