What I would do (and I am by far no EM guru). Start up a game and start manually pressing relay plates until I found the one that lights the bumper (if the labels are still there, it may be quickly discovered). Then clean and adjust the contacts on that relay.

Do you have a schematic? Without one I can only speculate but it's worth a shot.

One way a pop bumper with changing values works is with an Alternating relay. It's the relay that keeps track of which of two values the pop bumper has, and whether or not it's lit. It could be a simple relay with a switch stack, or the infamous AS style mini stepper relay. What happens is that when the pop bumper switch closes, a pulse goes through the Alternating relay and gets sent to either the 100pt relay or to the 1000pt relay. If the Alternating relay is a simple relay, it probably has a make/break switch (with three switch leaves - the long middle leaf switches between the two outer leaves). If the Alternating relay is an AS stepper, things are a little more complicated.

If you start a game, remove the ball and carefully lift up the playfield you can identify the Alternating relay by hitting whatever target toggles the pop bumper light on and off. You should see the Alternating relay change each time the pop bumper light toggles, or you might hear it clicking too. (Disconnect the chimes if that helps.) Note that the Alternating relay could be in the backbox too.

Once you've identified the Alternating relay, watch it carefully as you hit the target that makes it change. Do all the switches open and close as you expect? Are the switch stack screws tight? If you do have an Alternating relay with a make/break switch, it could be that one side (the 100pt side) is opening and closing as it should, but the other side (the 1000pt side) stays closed most of the time.

/Mark

To expand on Mark's answer, I would look for one of the make/break switches in the Q (alternating) relay. In one state, that switch is designed to route current to the 100-pt relay. In the other state, it should route current to the 1000-pt relay. I am guessing that in the one state, the center blade is making contact with the contact faces on both outside blades (that go to the L (1000-pt) and M (100-pt) relays), whereas, in the other state, it pulls away and is only making contact with ONE of the outer blades (that goes to the L relay).

However, I think there may be 5 M/B switches in the Q relay. You may have to consult a schematic to determine the wire colors on the M/B switch that energizes both the L and M relays. Alternately, you could inspect, clean, and adjust all the M/B switches in Q.

My previous comment was from memory as it has been several years since I had a King Pin in my collection.

Was doing some more thinking on it. What target/feature on the playfield turns the pop bumper lights on and off?
Was wondering if KP was one of those games that the pop bumper scoring depended on whether the machine was configured for 3-ball or 5-ball play (i.e. pops lighted and worth 1000 pts in 3-ball play and unlighted and worth 100 pts in 5-ball play)? If that was the case, then the alternating relay might only control the lighting of the holes, the standup targets, and the side rollovers. If that is the case, then your issue would not be due to the M/B switches in the Q relay.

Do you have the manual? If so, what does it say about pop bumper scoring values under the description of game play?

Check the operation & switch gaps on P relay-right & left pop bumper relay.

Would be helpful to check the schematic diagram. That would let you determine the circuits that are driving the L and M relays. Those should be located near the intersection of columns D to E and rows 5-7.

I would also look at the scoring reel operation before ruling them out.