We have this car in our barn . . .

SleepyBear said
So my husband just informed me that the button I remembered on the old Ford would have been the dimmer switch for the lights, not the washer fluid. So maybe there was an extra pedal down there at my feet I would pump for the water?? No matter - at 15, I was just tickled to finally learn how to drive, but I have to own up to my mistakes here with all you car experts!!
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No, your memory is better than his. The Falcons did have a manual washer pump in close proximity to the dimmer switch, unless they were optioned with an electric washer pump. Few early Falcons had electric pumps. I had two. a 64 and a 65. The 64 had the manual pump as you describe and the 65 had the electric pump.