Typically how long after a president's term do historians wait before starting to truly evaluate his time in office? How drastically can those views shift after time?
This is a fascinating question! How a historian assesses a president certainly varies over time. There have been presidents analyzed and ranked during their time in office, particularly quite recently. How a president is viewed often changes over time as they enter the mythos of commonly repeated American history(or perhaps myth) or fade into obscurity.
My first example will be Chester Arthur, who was often lauded in his time by historians and the common person. Arthur was cast adrift within his party but his show of independence won him a measure of respect and led to him being ranked fairly well by historians and ranked quite highly by people. Biographer Alyn Brodsky points out that Grover Cleveland was often ranked near the top of presidential rankings by historians and common people alike in between his terms and in the decades immediately following his time in office. Cleveland has faded into relative obscurity though and now often falls much lower in presidential rankings.
Some presidents are seen quite positively in office and historically such as President Washington or President Lincoln. Others such as President Kennedy are much more popular now than during their term. The corruption of the Grant administration often lowers it’s rankings among historians and for good reason, but he was fairly popular until the extent of the Whiskey Ring was revealed. President Hayes was quite unpopular upon ascending to the presidency but became more popular, yet his unpopular follows him historically due to the Compromise of 1877.
Presidents are generally viewed either much more negatively or much more positively in the immediate aftermath of their administration compared to how they are viewed historically and within hindsight. Benjamin Harrison, a man who nearly always is ranked near the middle of presidential rankings, was of course a polarizing figure in his time and ranked as being better or worse than he is seen today by contemporaries as they had a more immediate image of him which causes biases.