So played around a little more, it seems that the +12V has to come up first (that we knew already), but the -12V has to come pretty soon afterwards. If the -12V is a little later, then the probe indicates "overheating". If both -12V and +12V come up exactly at the same time, no indication what so ever. If the -12V comes up first, you get exactly the same result as with both +-12V together.
More in details together with current consumption:
1) first +12V, very soon after -12V => probe start up correctly with automatic degauss
+12V: 151mA // -12V: 145mA (remark: during automatic degauss: both +-12V approx. 600mA, after degauss, for a few seconds +12V:164mA // -12V: 158mA until relay clicks in probe, then to 151mA&145mA)
2) first +12V, one second later -12V => immediately indicates "overheating", then probes performs automatic degauss, ,and after that does not react on button presses.
+12V: 164mA // -12V: 158mA (remark: during automatic degauss: both +-12V approx. 600mA). When +12V only => 800mA! (could this trigger the overheating?) No relay click in probe after degauss. Remains in same current as successful start-up before relay click in probe. Probably does not switch to its final state due to overheating error.
3) +12V and -12V exactly at the same time => probe does not start up (no automatic degauss, no reaction on button presses)
+12V: only 17mA // -12V: 310mA
4) first -12V and then +12V => probe does not start up (no automatic degauss, no reaction on button presses)
+12V: only 17mA // -12V: 310mA. Exactly the same behaviour as both +-12V at the same time
So I do not think it is some kind of thermal latch up, as I can repeat the above as much as I want, it behaves always the same.
So for me it seems when the internal microcontroller gets power (powered from the +12V rail), it tries to start the degauss. When the -12V is not present at that time, the degauss function consumes 800mA from the +12V, and the overheating flag is set. When the -12V comes on, the degauss function continues normally, but because the overheating flag is already set, the probe start-up sequence does not finish successfully. This behaviour seems still normal to me.
What was strange however, if the -12V is present at the moment the microcontroller tries to start up (when the +12V arrives), there is no start-up sequence what so ever. So I think we need to look at how the -12V could inhibit the microcontroller (MC705P6ACDWE) from starting up.
The reset pin (pin1) would be the obvious suspect. It is tied to the 5V of the 78L05A (next to the keyboard connector), and when the -12V comes on first, no 5V to thin pin is supplied. So that is a problem for sure!
It seems that the 7808 regulator is completely overloaded when the -12V comes on first (output voltage is at -0.8V, so somehow the -12V (or -8V) is tied to the +8V output of this regulator when the negative supplies come on first.
I will look further into this a bit later, but for now, I have to do some other job.