Hi,

The throttle cable is a very reliable component but it can still wear out.
This item wears on the inside of the sheath completely out of sight.
The cable is made with strands of steel wire that can wear more in one area or side than another.

Oiling the cable with this amount of age will not help unless its clogged with dirt.
Dirt is a ingredient that can cause these strands to fray and thus start dragging on the insides of the sheath. When this happens the strands are not being contained in a tight round formation.
Random jamming can occur.

One has to remove the cable. It is best to do this from both ends and work the cable back and forth with no load. Some people undo the engine end first and see it they can move the pedal freely but the cable shifts. What ever procedure expect only a completely smooth back forth action. Any snagging will only be worse under the loading of the return spring on the throttle cable spool.

If I were you, get a hold of another cable unit. Since you may be removing the one in the car, you will have it on hand to compare them to each other under the same conditions.

The newer one can be off a junker or a totally newone as its your choice.
How long are you planing to keep the car is part of that equation.

Good luck

Phil