Replay: the credit unit is stepped up by one, and you hear a knock.
Extra ball (on a multi-player game like Royal Flush): The "same player shoots again" relay is turned on, one of its functions being to light the corresponding light on the playfield. When you drain that ball, the relay stays on long enough to suppress the usual end-of-ball step ahead to the next player or ball in play.

If your photo shows the Credit Unit (the one with a reel to display how many credits you have through the little window), then I think you are showing us the hack that allows free play even when there are 0 credits. That would be unrelated to your problem.
.................David Marston

I can see some terminology overlap between:
Free Play: does not require a coin to start the game even when there are zero credits;
Free Game/Replay: a credit won by skillful play.
Special: a euphemism for replay (as defined above) in most territories, but can mean other awards, including extra ball, in places where replays are outlawed.

Some Bally multi-player EM games were described as being "convertible to add-a-ball" where the Special and scoring thresholds would turn on the Same Player Shoots Again relay. Search for the topic words "add-a-ball" in this forum to find several topics that discuss why such behavior is not considered "true" add-a-ball.

So I gather that your game is BOTH set for free play (as defined above) and has some hack that was attempting to implement Bally's idea of an add-a-ball conversion. Besides a knock, is anything happening when you reach the designated number of points for a reward?
.................David Marston

Those number-match steppers don't have a home position, they just cycle around. They are notorious for adjustment issues such as being unable to step forward. Even if the game is set for free play, a match could still award a game on the credit unit. But if your game was hacked to give an extra ball at certain point scores, that hack could interfere with the match circuit, too.

When you light and then win Special, what do you get?
.................David Marston

When you get the knock, is the credit wheel also stepping up by one step? Normally Gottlieb makes the knock a by-product of this wheel stepping up, but I think it is safe not to assume anything. The step-up and knock should occur for all 3 kinds of win: score threshold, end-of-game match, and special. (Side note: when the game is priced to give multiple games for a quarter, inserting the quarter will cause the credit unit to step up, but the knock is suppressed.)
.................David Marston

The only switch on the credit unit that defeats the step-UP (or "add") solenoid is the one that opens when the maximum number of credits has been reached. You should do your experiments with 2-3 credits showing when you start, so you can observe steps in either direction.
.................David Marston

I hope "correctly" means that numbers are showing through the window. That first photo of the reel being in thte blank area above 15 is a place the reel should not be.

Of the two posts in the side of the ratchet, the one with a screw head that can be taken out and put in one of several threaded holes is where you adjust the maximum number of credits allowed. The fixed post is the one that is supposed to actuate the zero-position switches.
.................David Marston

There is an extra pawl on those stepper units for single-step subtract. It could be held out of the way, which would allow a full fly-back instead of a single step. Look at all the things that engage the ratchet teeth and you may be able to pick it out.
.................David Marston