If you undo the front nut,
You will see the seal inside. It is like a long graphite seal.
Once this is off you can undo and slide the needle out. You need to unscrew it by turning it to the left ( like turning it on ).
Close up of the needle base. This also has a brass washer on it.
Front pic of where the needle seats. This is where part of the seal gets gummed up.
Clean it up, reassemble nipping it up tight and bob should be your sister with no more leaks
Note: when you put the front sealing nut back on and tighten, have the on/off knob half to three quarters open as the sealing nut will want to tighten the needle as it goes.