I realized that I've had several Pat Lawlor games and not looked for the Red button. To date I've owned: TZ, Whirlwind, Banzai Run, Safe Cracker. In Funhouse, it's the classic button on a stick. Here's what I found just viewing a friend and looking at my own games. Please correct my mistakes.

Post a pic and the location of the button.
Banzai Run: next to the throttle.

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Safe Cracker: look at the truck.

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Funhouse: In Rudy's hand.

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NASCAR: just in the little PLD logo. It's hard to see in the photo, but it has a little hand with a button.

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Great find. I’ve owned a Safecracker and didn’t remember spotting that coin.