looking at the schematic page one (page 2 is pretty well the same only with the switching facilities) , think of this circuit in three major parts:
1) there is a power supply (yes I know, bear with me here) in the top left hand corner - this generates +12V, -12V, -6V and a +2.5V reference (off the TL431).
This consists of N3, V1A, V2A, V3A, V4A, V5A, V6A, V7A and associated R's and C's and is power by Transformer windings N5
2) Voltage regulator circuitry below this which regulates the main output and provides current limiting and voltage regulation - this uses 2.5V off V5A as a reference voltage and the active circuitry is powered by section 1.
This consists of N1 and N2 V20, V21 and V22 - V11A V12A V13A, V14A and is powered from Taps N2, N3, N4.
the transformer tap is selected by section 3 - depending on the output voltage
3) tap selector circuitry - this changes transformer taps for the power supply to minimise heat dissipation on the regulator pass transistors. it switches to a lower voltage tap when the output drops - either because the output voltage is set low, or because the current limit is limiting the output voltage.
This consists of N4A, N4C selecting either Relay K1A or K2A via Transistors V25A or V26A.
ok if the tap switcher (section 3) was changing incorrectly I would expect the output voltage to stay in regulation, so my main suspicion would be that the relays are switching because the output is changing rather than the other way around.
potentiometers often get noisy so I would first suspect the pots W6, W6A, W5 and W5A - maybe W8. measure the voltage coming off these (say at the junction of R54A and C13A) see if this varies.
the reference voltage could also be faulty as could the power supply rails from section 1, so I would also check the supply rails from section 1
I understand this is a dual power supply (ok, triple if I include the 5V rail) I presume when running in independent mode that only one rail is playing up?