The "skill lane" is used when operating the game in 5-ball mode. After WW2 the law started cracking down on 1-ball games so Bally started making their 1-ball games convertible to 5-ball games. To skirt around the laws that were specifically against 1-balls.
Instruction on how to convert your 1-ball to a 5-ball are covered in your manual. You need 4 more balls (don't use that brass thing) and a special ball gate (it and the balls were originally included with your game) to replace the rebound rubber/bracket. This bracket allows the first 4 balls to enter the small trough under the red cover, and rebounds the 5th ball away like the rubber does. The idea is you use your "skill" to shoot the first 4 balls into the skill lane (the skill to pull the plunger all the way back and release) the 4th ball landing in the trough operates a switch that allows the 5th ball to score, if you land in a lit hole, of course.
Most of the skill involved in playing the 1-balls is learning which number holes the ball has a tendency to land in (the balls tend to gravitate toward the center of the playfield so numbers like 3-4-5 are your best chances, then 6-2, 1-7 not very often) and to play enough coins/credits to get the appropriate numbers lit, either directly or thru the wild sections lighting up. And getting the odds up high enough that if you do win, youll get back more than you spent.
If you won (and the location knew you well enough) you could ask the proprietor to pay you off (usually a nickel a credit) and after you were paid the proprietor could clear the credits from the game. Either by turning the game off and then on again, or by pushing a button on the under side (in the alcove) of the cabinet.
In looking at the pictures of your game, it appears you may have a "Frankenstein" made of 2 or more different Turf Kings. Your cabinet has the coin entry above the door and the coin entry and shooter housing are cast pieces. These were found on the early production (no AB prefix on the serial #) games, which had the feature hole score advance via a stepper unit (like a replay stepper with a drum with small numbers, visable thru the backglass) mounted in the games head, to the right of the replay register. The later production games (with the AB prefix serial #) had a set value for the feature hole, adjustable thru a plug on the slide out mechanism panel, towards the back, past the mixer unit. Also, the later ones coin entry and shooter housing were a stamped out type, rather than cast. Its not serious but may require a few changes at the jones plugs to adapt.
Your Turf King does appear to be in pretty nice shape cosmetically. A couple of pinsiders emailed me suggesting I go get it, But Ive got enough 1-ball games and parts here already, so I passed on it despite its (sorta close) proximity to me. I'm in SLC too.