Try adjusting (ie bending) that metal plate kicker a little.

So, the mechanism that smacks the ball is compromised (flattened). Marco sells a replacement part:

https://www.marcospecialties.com/pinball-parts/A-8247

The pivot point with the shaft that this part rotates on is actually one of the only places you put a drop of oil. I've found these mechanisms can be very stiff due to lack of oil. I remove the assembly from the bottom of the playfield, take it apart, clean the old grease off, and apply fresh oil. Sometimes the shaft this rubs on is deeply grooved due to wear, and it needs to be replaced, but frequently oiling this appropriately works good.

Because this is an Addams Family, and Addams Family pinballs have generally had a LOT of work through the years, the spring on this assembly might have been replaced with a spring that is too weak. In the picture everything looks correct, but this assembly uses a quite stiff spring, and a lighter spring doesn't apply nearly enough 'smack' to the ball. I don't think this is your problem.

For other pinballs, you need to make sure that the part is actually hitting the ball squarely, because on other pinballs they don't get enough play to flatten the end. Your assembly looks properly aligned.

Finally, on the top of the playfield there is a little metal extension that 'curls' the ball back to the shooter. This is a frequent point of adjustment, and I'm wondering if that metal piece that when the ball is popped guides the ball to the shooter rod is mis-adjusted. When the ball does pop up, it should strike this metal extension and be guided to the lane back to the ball shooter rubber tip. When it's mis-adjusted it can prevent the ball from going into the lane, or allow the ball to pop up, hit the side rail, and drop right back into the ball popper area!

Do all of this. Also check for dry crusty oil causing the mech to hang up. I have had them where the "hook" was extending the spring half was before it even made contact with the ball and then getting stuck there for the second or third try because of old lubricant. Also as stated previously, your "hook" is mushroomed and at the very least needs to be taken apart and ground down but more likely replaced. The mushroomed top can hit on the edges of the hole or the switch and cause the ball not to eject.

I'm always amused by lights in pinballs...

Ok, I have eight lights out, and they are all connected to the -yellow-green- wire...

(After trying everything possible for an hour tracing the yellow-green wire...)

Nope. All eight bulbs are burnt out.

Hehe.

As part of my standard 'shop' of an Addams Family I pull all the lamp boards and refresh the solder at the connectors. It's so common to find a cracked solder connection causing half the board of lamps to not come on.

I also find myself doing this kind of troubleshooting when I've got lights out on the green boards with the 555 twist-in sockets:

I pull out a non-lighting bulb, I find another bulb that is lighting, I untwist it, and put the (known working) bulb in the suspect lamp hole.

The reason for this is that it is extremely common for the two little fingers on the black sockets to not make good connection to the printed circuit board, and it's extremely common to have the little wires on the bulbs not make perfect connection inside the little black socket. Putting a known good black-socketed 555 into the suspect hole on the board speeds up my troubleshooting.

For most of my Addams Family pinballs, it's actually rare for me to have to do anything with the lamp circuitry. If ALL the lamps are out I've replaced the associated bridge rectifier a bunch of times, but if it's just particular strings of lights being out, I usually solve my problems with replacing an insane number of burnt out bulbs, and re-soldering the connections on every green lamp printed circuit board.

Let us know what you find!

Yup. Check the simplest stuff first. The first pin I bought, way back when, was (still is) a High Speed. The seller explained there were some problems but he didn't feel like working on it (he had a whole route of other pins to deal with). One of the problems was that neither of the blue flashers in the middle of the playfield worked. He suggested I look at things like the transistors, connections, etc.

Well, I did all that, didn't find a single thing wrong. Took forever too, in spite of a modicum of experience with electrical/electronic stuff, because I was brand new to pinball.

Eventually, I took a look at the bulbs. Sure enough, half the bulbs in the flashers were burned out. Turns out, there are pairs of bulbs in series, so when one goes, the other won't light up any more. Have that happen a couple of times, now all your blue is gone!

Sigh. Reminiscent of the time I spent hours trying to figure out why my car ran so rough for 10-15 minutes, came up with all kinds of cockamamie theories based on hydraulic lifters or thermal expansion of rings or whatever. Finally, just replaced the spark plugs, and all was well again.

I always check the most basic, easiest to deal with things first now.