In every instance when I have experienced this (my 1980 TR8 and on my '05 Jeep Wrangler), it was the rear control arm bushings worn out allowing the rear axle to move around that caused it. In both cases when you accelerated the car pulled to one side and when you lifted it pulled the other way. This is where I'd start looking.
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Dave S.
2003 Boxster S
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