What caused this tree resin, emerging where a branch was sawn off, to flow out at an angle, then vertically downwards, before flowing in an upward curve (see photo)?
I maintain that is does not flow out at an angle, but hardens on the surface nearer the sun (as in the picture). The softer side away from the sun flows a bit more, causing the end of the "branch" to eventually point upwards.
I suspect with these thinner flows of sap, the strand grows from the base rather than the free end. As the sap gets squeezed out of the trunk, it would start to harden. If the hardening is not even all around the column of the sap 'strand' it will slowly curve.I suspect that the opposite is true to what the commenter above said - I think the warmth of the sun will make the sap softer and runnier, which is why the strands are bending away from he trunk. I know from experience that when you take some sap off a tree like that, if it's not completely hard already, then it does get softer as it warms up to body temperature.
The sap comes out of the tree and hardens into a blob. This is then pushed away and up by more sap coming out in a liquid form. This generates an upward curve.Once the extending stick of resin becomes heavy enough its weight is sufficient to weaken the base and allow further growth to be on the top side. Eventually the whole thing turns downward.This can be seen in the picture, the short pieces are pointing upward and growing either up or horizontal, the longer ones hang down. The really long one appears to have been bent down at some point, the resin is not truly hard for a very long time.