It's a compression gasket basically.
The end of the nut facing the packing is rounded and when you screw the nut in,it push's the packing against the needle to seal it. The more you tighten the more it tries to squish against the needle.
The old one's were like the old "rope" seals used on rear mains on motors.
Graphite impregnated cotton.
IF you could find a "O" ring that fit the needle,that might get you thru.
Or, a rubber faucett washer from a faucett rebuild kit from the hardware store.You'd have to cut it down to fit,but when your in a bind.....