On my 1998 base Boxster the headlights are never "ON" unless I turn them on. The 98' does not have "daytime running lights" unless someone, like a previous owner, has done some sort of modification.
Since you are a "new owner"...(forgive me for asking the obvious, but....) are you sure you have the light switch on the left of the steering wheel in the "OFF" position??? If so, then my best guess is that a previous owner did some sort of modification.
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98' Boxster
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