It looks to me like the jumper between the W relay and the S relay is a misguided attempt to put the game on free play. If I had to guess, what they did was to re-wire the extra chute coin switch on the coin door onto the replay button. But, as jasonspoint28 noted, since the game was adjusted to only add 2 credits for each coin switch closure, moving that coin switch wire to the replay button didn't actually start a new game. So to fix that, they jumpered the W relay signal wire to the S relay signal wire, so that pressing the replay button would trigger the S relay. But that also triggered the W relay, so they clipped the black wire from the W relay to prevent the W relay from firing. Yikes.
Needless to say, this is not the easiest way to put a game on free play.
EDIT: I pulled out my Fun Land schematic, and based on that, it shows that this game has the combined 1st & 2nd chute adjustment plug, not the one shown in post #18 above. So, you will probably need to change the wiring on the coin door so that it is back the way it is supposed to be if you want to remove the jumper between the W and S relays. That may be a way you can go, if the coin door wiring hasn't been hacked up too much.
The coin door should have a common orange wire going to one side of every coin switch, and also to one side of the replay button. If the coin door is still wired to factory spec, there will be a brown wire on the other side of the replay button. For the coin switches, there will be a blue wire, a yellow wire, and a green wire going to the other side of each of the coin switches (depending on how many coin switches your door has). If you door is wired differently than this, it has been hacked.
I suspect that someone jumpered the green wire (extra chute coin switch wire) to the replay button where the brown wire should be. If that is the case, you can remove the green wire from the replay button, and re-attach the brown wire. Then you'll need to permanently close the switch on the replay unit that opens at zero to shut off the replay button. Once you do that, your game should properly be set on free play. At that point, you can remove the jumper between the S relay and the W relay, and resolder the double-black wire to the W relay coil.
If the coin door wiring has been hacked such that you can't easily follow the above description (it happens more than you might think) please let us know and maybe post pics of the door wiring so we know what you're dealing with.
No matter what else you do or don't do with your game, it is absolutely essential that you confirm that the clipped double-black wire at the W relay lug has the two black wires solidly soldered to each other. This is THE main daisy-chain return wire for every coil, and if those two wires become separated, that would absolutely knock out one or more important functions on your bottom board.
By the way, none of this has anything at all to do with your knocker problem, except for a possible issue with the W relay knocker mute switch, which might not be making good contact. But that would be more of a coincidence rather than a direct root-cause connection. Any time the W relay is not pulled in, that mute switch should be making solid contact, allowing the knocker to fire. Since the W relay never pulls in if it is disconnected, that W relay switch should always be closed. But it may not be making good contact, which would prevent your knocker from sounding.