With the crook removed from the body, finger an octave A and grip the little pin that stick up above the crook socket. Try to move it up and down. Does it move freely, with no sense of stiffness or sluggishness?
Now finger an octave G and repeat. Does this make any difference?
If all is well then it's likely your octave mech is fine - and either the spring on the crook key has failed...or the pads are sticking.
If there's some sluggishness it might simply be down to a lack of lubrication. Some oil will help, but if the existing oil has dried it might be fouling the mechanism. A strip down would be the fix, but a good 'get by' is a couple of drops of cigarette lighter fluid place on the junctions where the key barrels meet, and where they butt up against the pillars.
One other test you can do is to get a small screwdriver and give the octave key mech screw a turn back and forth. Watch the mech as you do so to see if the whole thing rises and falls. If so this would indicate a bent rod screw.
If it doesn't do this, but a single key on the group moves as you turn the screw then it may mean one of the keys is bent.