I know with my 1962 Williams King Pin the two playfield rollovers that controlled Spares stayed lit the entire time of the game. Hopefully someone can chime in with your specific game.
However my 1964 Williams Heat Wave two rollover buttons were controlled by the Advance Stepper Unit in the back of the Head which would leave them on in the beginning of the game but shut them off completely when the temperature gauge advanced a certain amount of degrees to make the game harder to advance the temperature as you played. Looking from pictures on the IPDB it looks like yours does turn on and off at certain points in the game. I do not have a schematic but check the Stepper Unit to make sure it is functioning correctly, wires intact, and snowshoes contacting rivets correctly.