Preface: My dad owns a functioning Grand Tour. I'll get some plays in this weekend to confirm operation. Without looking at the Thumper Control Unit Stepper in person or having a good picture of the wipers this is my best guess.
Looking at the score motor switch chart the following switches apply to the Thumper Control Unit Stepper:
1A-a: Pulses replay unit and thumper control unit step-up coils or, 100 point relay thru advance feature replay or point scoring unit
1A-b: Pulses replay unit and thumper control unit step-up coils thru match number replay scoring unit
2C-c: Pulses replay unit reset coil, total play meter and thumper control unit reset coil thru start relay circuit
Based on this information, the Thumper Control Unit is controlled by the Advanced Feature Replay Unit, the Point Scoring Unit, the Match Number Replay Scoring Unit and the Start Relay Circuit
The following switches apply to the Advance Feature Replay Unit:
1B-a: Subtracts a pulse from score motor switch 1A-a during replay step-up for multiple play coin circuit and advance feature replay or point scoring circuit.
2C-a: Subtracts a pulse from score motor switch 1A-a during advance feature replay or point scoring circuit.
3B-a: Subtracts a pulse from score motor switch 1A-a during replay step-up for multiple play coin circuit and advance feature replay or point scoring circuit.
4C-a: Subtracts a pulse from score motor switch 1A-a during replay step-up for multiple play coin circuit and advance feature replay or point scoring circuit.
The number of switch pulses per score motor rotation:
1A-a is pulsed 5 times per score motor rotation
1A-b is pulsed 5 times per score motor rotation
1B-a is pulsed 1 time per score motor rotation
2C-a is pulsed 1 time per score motor rotation
2C-c is pulsed 1 time per score motor rotation
3B-a is pulsed 1 time per score motor rotation
4C-a is pulsed 1 time per score motor rotation
Switch 1A-a pulses the Thumper Control Unit Step-Up coil once per score motor rotation due to switches 1B-a, 2C-a, 3B-a, and 4C-a subtracting once pulse each from the 5 pulses of switch 1A-a. This can happen after a players earn a high score or an advance replay
Switch 1A-b pulses the Thumper Control Unit Step-Up coil once the Match Number Replay circuit is activated at the end of a 3 or 5 ball game. This can happen after a players earns a match replay
Switch 2C-c pulses the Thumper Control Unit Reset coil once per score motor rotation once the Start Relay coil is activated. This can happen when a new game is started or when you put money in the machine
To summarize, if a player earns an advance feature replay or a hi-score, the Thumper Control Unit will step up once by way of switch 1A-a.
If a player earns a match number replay, the Thumper Control Unit will step up once by way of switch 1A-b.
At the start of a new game or when money is put in the machine, the Thumper Control Unit will step down once by way of switch 2C-c.
This would appear that the machine is designed to be more difficult based on previous plays of the machine. Given that these machines were made to empty the nickels and dimes from its victims I wouldn't be surprised if that was the case. See this post which I believe describes the intent of this setup.
https://pinside.com/pinball/forum/topic/em-tech-bally-mad-world#post-1998180
As a side note: If I had to guess, your machine hi-score adjustment is set to 500 and that is why it is stepping up when you hit 500 points.
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