Here's the corresponding diagram for Durham North if it helps:
https://signalbox.org/~SBdiagram.php?id= 830
For the main signal to clear, the track would have to be unoccupied at least as far as the next main signal and probably beyond, depending on how "clearing points" worked in this area. A depression bar only proves the track clear within its own length, so this situation would need a track circuit (or, in more recent times, an axle counter) and I somehow doubt the state of a track circuit would lead to a different arm being cleared in that era.
I'm wondering if the main arm would only clear if Durham North had pulled its distant off, possibly due to no clearing point beyond the north end of the platforms. This might also explain the subsidiary arm clearing with the main arm - if it didn't then the subsidiary would have to drop back to danger when North cleared its distant and allowed the main stop arm to clear, which might be difficult to arrange in a slotting mechanism and/or confusing to drivers. But as
@zwk500 has mentioned above, there is no indication of any slotting on the main stop arms.
Edit: I've also read somewhere that you would occasionally find three-position levers, and thinking some more I think that may be the answer and what the little 1 and 2 are seeking to convey. Pulling the lever to its first detent would require the locking conditions for the subsidiary route and clear only the subsidiary arm, but pulling it to position 2 would also require additional locking conditions if any, possibly the block instrument from North, or the signalman was trusted not to pull it to this position unless the platform was clear and North had given an unrestricted acceptance through to the clearing point beyond the station. Again, if the subsidiary arm cleared only in position 1, then pulling the lever all the way to position 2 would cause it to clear and immediately drop back, which doesn't seem like good practice and would explain why it would remain clear in position 2.