The Contact Finger Assembly shown on your catalog page mounts to the inside of the rotating score reel and wipes over the Contact Disc Assembly (also shown). These two parts make up a rotating switch that the game uses when it needs to know what digit is showing. This arrangement is typically used by the match circuit but in your game it is used to fire the Change relay:

Friendship 7 score reel (resized).jpg

As the score reel rotates it make and breaks the circuit that fires the Change relay. The ground wire provides continuity to the Contact Finger Assembly which in turn makes contact with various rivets on the Contact Disc.

Note that the ground wire function is only necessary on score reels with a Contact Disc Assembly. The rest of the score reels just need a mechanical (not necessarily an electrical) clip to keep the reel from falling off the axle.

/Mark

In the short term, I'd move an available ground wire from another score reel to the score reel with the Contact Disc if necessary, then make one from stiff wire or even a paper clip for the score reel with no Contact Disc.

You might also have luck asking here: https://pinside.com/pinball/forum/topic/the-em-seeking-parts-thread