From my knowledge the aircraft is supposed to spin to the right when left stick is applied.
It doesn't really seem right, but when you put the stick full left the right aileron is going to go down. The right aileron going down increases the angle of the "chord"(attached image) of the right wing, thus increasing the angle of attack on the right wing and decreasing the angle of attack on the left. Stalling is caused by the angle of attack of the "chord" of the wing being too great, so the wing stalls. Because the angle of attack is higher in the right wing with full left stick, it will stall first, thus the spin to the right.
Also you might be able to help the aircraft spin by pushing the rudder in the direction of the desired spin while turning the ailerons the opposite direction.
This may not be correct with the F-86, but its just my knowledge from spins in cessnas/pipers.
Hope I could help!