I don't have a Top Card schematic to look at right now but as I recall, the target scoring is done via a relay called something to that effect (Target Value Relay?). There are usually two ways Gott. did scoring on multiple targets like that. There is usually a "Series" relay. A relay coil that is common to all the other trip bank relays. In some games, the trip bank coil will energize with each hit (along with the series scoring relay). In other games, there is a make break switch that first, allows power to the trip bank coil, and then, once tripped, routes power to the score relay. If it is a series relay, it is a special winding/value since it is in-line with the power going to each trip relay. It is always possible that someone replaced the coil with the wrong value and now, it is not sensitive enough to trip.
Also, as I recall, target scoring is a score motor function even though it is scoring a single value like 10, 100 or 1000. So, a hit to a target, should energize the target score relay which in turn, starts the score motor which does the actual scoring.
As to a stuck outhole kicker, that is a strange one since there are normally a number of switches that would need to be "made" in order for it to turn on (as you already listed). If the score motor switch were stuck, it would only energize when the outhole relay is pulled in. If the Outhole relay switch were stuck on, it would only energize with a turn of the score motor. So, you may be looking for something like a nut or washer lodged under a Jones plug connector. Or a solder splash on the side of a switch stack. Or a relay lug being bent over to touch another lug.
Is the outhole coil energized the minute you turn power on to the game? or only after you hit the start button?