Eight top presidential vote shares (from 1836 on) in every state (as of October 1996)

(Only the states in which at least one of the top eight vote shares is from one of the last seven elections appears here. This is the parent post.)

California
Franklin Roosevelt, 1936: 66.95%
Warren Harding, 1920: 66.20%
Herbert Hoover, 1928: 64.69%
Theodore Roosevelt, 1904: 61.84%
Lyndon Johnson, 1964: 59.11%
Abraham Lincoln, 1864: 58.60%
Franklin Roosevelt, 1932: 58.39%
Ronald Reagan, 1984: 57.51%

Connecticut
Lyndon Johnson, 1964: 67.81%
Dwight Eisenhower, 1956: 63.72%
William McKinley, 1896: 63.24%
Warren Harding, 1920: 62.72%
Calvin Coolidge, 1924: 61.54%
Ronald Reagan, 1984: 60.73%
William Howard Taft, 1908: 59.43%
Richard Nixon, 1972: 58.57%

Delaware
Herbert Hoover, 1928: 65.03%
Lyndon Johnson, 1964: 60.95%
Ronald Reagan, 1984: 59.78%
Richard Nixon, 1972: 59.60%
Horatio Seymour, 1868: 59.00%
Calvin Coolidge, 1924: 57.70%
Grover Cleveland, 1884: 56.55%
George H. W. Bush, 1988: 55.88%

Idaho
William Jennings Bryan, 1896: 78.10%
Ronald Reagan, 1984: 72.36%
Ronald Reagan, 1980: 66.46%
Theodore Roosevelt, 1904: 65.84%
Warren Harding, 1920: 65.60%
Dwight Eisenhower, 1952: 65.42%
Richard Nixon, 1972: 64.24%
Herbert Hoover, 1928: 64.22%

Illinois
Warren Harding, 1920: 67.81%
Dwight Eisenhower, 1956: 59.52%
Lyndon Johnson, 1964: 59.47%
Richard Nixon, 1972: 59.03%
Calvin Coolidge, 1924: 58.84%
Theodore Roosevelt, 1904: 58.77%
Franklin Roosevelt, 1936: 57.70%
Herbert Hoover, 1928: 56.93%

Indiana
Richard Nixon, 1972: 66.11%
Ronald Reagan, 1984: 61.67%
Dwight Eisenhower, 1956: 59.90%
George H. W. Bush, 1988: 59.84%
Herbert Hoover, 1928: 59.68%
Dwight Eisenhower, 1952: 58.11%
Franklin Roosevelt, 1936: 56.63%
Ronald Reagan, 1980: 56.01%

(George W. Bush's 56.65% in 2000 would have been #7 until 2004, and #8 from 2004 until 2016. Trump's 56.82% in 2016 would have been #8 from 2016 to 2020.) 

Kentucky
Horatio Seymour, 1868: 74.55%
George McClellan, 1864: 69.83%
William Henry Harrison, 1840: 64.20%
Lyndon Johnson, 1964: 64.01%
Richard Nixon, 1972: 63.37%
Samuel Tilden, 1876: 61.41%
Ronald Reagan, 1984: 60.04%
Herbert Hoover, 1928: 59.33%

(George W. Bush's 59.55% in 2004 would have been #8 from 2004 until 2012. Romney's 60.49% would have been #7 from 2012 until 2016.)

Maryland
Horatio Seymour, 1868: 67.20%
Lyndon Johnson, 1964: 65.47%
Franklin Roosevelt, 1936: 62.35%
Franklin Roosevelt, 1932: 61.50%
Richard Nixon, 1972: 61.26%
Dwight Eisenhower, 1956: 60.04%
Franklin Roosevelt, 1940: 58.25%
Herbert Hoover, 1928: 57.06%

Massachusetts
Lyndon Johnson, 1964: 76.19%
Abraham Lincoln, 1864: 72.20%
Ulysses Grant, 1868: 69.76%
William McKinley, 1896: 69.47%
Ulysses Grant, 1872: 69.20%
Warren Harding, 1920: 68.55%
John Frémont, 1856: 63.61%
Hubert Humphrey, 1968: 63.01%

Montana
William Jennings Bryan, 1896: 79.93%
Franklin Roosevelt, 1936: 69.28%
Warren Harding, 1920: 61.13%
Ronald Reagan, 1984: 60.47%
Dwight Eisenhower, 1952: 59.39%
Lyndon Johnson, 1964: 58.95%
Franklin Roosevelt, 1932: 58.80%
Franklin Roosevelt, 1940: 58.78%

Nebraska
Ulysses Grant, 1872: 70.68%
Ronald Reagan, 1984: 70.55%
Richard Nixon, 1972: 70.50%
Dwight Eisenhower, 1952: 69.15%
Ronald Reagan, 1980: 65.53%
Dwight Eisenhower, 1956: 65.51%
Rutherford Hayes, 1876: 64.70%
Warren Harding, 1920: 64.66%

New Mexico
Franklin Roosevelt, 1932: 62.72%
Franklin Roosevelt, 1936: 62.69%
Richard Nixon, 1972: 61.05%
Ronald Reagan, 1984: 59.70%
Lyndon Johnson, 1964: 59.22%
Dwight Eisenhower, 1956: 57.81%
Franklin Roosevelt, 1940: 56.59%
Harry Truman, 1948: 56.38%

New York
Lyndon Johnson, 1964: 68.56%
Warren Harding, 1920: 64.56%
Dwight Eisenhower, 1956: 61.19%
Franklin Roosevelt, 1936: 58.85%
Richard Nixon, 1972: 58.54%
William McKinley, 1896: 57.58%
Calvin Coolidge, 1924: 55.76%
Dwight Eisenhower, 1952: 55.45%

North Dakota
Warren Harding, 1920: 77.79%
Theodore Roosevelt, 1904: 75.12%
Dwight Eisenhower, 1952: 70.97%
Franklin Roosevelt, 1932: 69.59%
Ronald Reagan, 1984: 64.84%
Ronald Reagan, 1980: 64.23%
William McKinley, 1900: 62.12%
Richard Nixon, 1972: 62.07%

(George W. Bush's 62.86% in 2004 would have been #7 until 2016, and #8 from 2016 until 2020.)

Oklahoma
Richard Nixon, 1972: 73.70%
Franklin Roosevelt, 1932: 73.30%
Ronald Reagan, 1984: 68.61%
Franklin Roosevelt, 1936: 66.83%
Herbert Hoover, 1928: 63.72%
Harry Truman, 1948: 62.75%
Ronald Reagan, 1980: 60.50%
Richard Nixon, 1960: 59.02%

(George W. Bush's 60.31% in 2000 would have been #8 from 2000 until 2004.)

Rhode Island
Lyndon Johnson, 1964: 80.87%
Ulysses Grant, 1872: 71.94%
William McKinley, 1896: 68.33%
Ulysses Grant, 1868: 66.49%
Hubert Humphrey, 1968: 64.03%
Warren Harding, 1920: 63.97%
John Kennedy, 1960: 63.63%
Abraham Lincoln, 1864: 62.241%

South Dakota
Theodore Roosevelt, 1904: 71.09%
Dwight Eisenhower, 1952: 69.27%
Franklin Roosevelt, 1932: 63.62%
Ronald Reagan, 1984: 63.00%
Warren Harding, 1920: 60.74%
Ronald Reagan, 1980: 60.53%
Herbert Hoover, 1928: 60.18%
William Howard Taft, 1908: 58.84%

(George W. Bush's 60.30% in 2000 was #7 until 2016, and his 59.91% in 2004 was #8 until 2016. Between 2016 and 2020, his 60.30% in 2000 was #8. In this case, his percentage went down in 2004.)

Tennessee
Franklin Roosevelt, 1936: 68.85%
Ulysses Grant, 1868: 68.43%
Richard Nixon, 1972: 67.70%
Franklin Roosevelt, 1940: 67.25%
Franklin Roosevelt, 1932: 66.49%
Franklin Roosevelt, 1944: 60.45%
Samuel Tilden, 1876: 59.79%
Hugh White, 1836: 57.92%

(Romney's 59.48% in 2012 was #8 until 2016.)

Utah
William Jennings Bryan, 1896: 82.70%
Ronald Reagan, 1984: 74.50%
Ronald Reagan, 1980: 72.77%
Franklin Roosevelt, 1936: 69.34%
Richard Nixon, 1972: 67.64%
George H. W. Bush, 1988: 66.22%
Dwight Eisenhower, 1956: 64.56%
Gerald Ford, 1976: 62.44%

Washington
Theodore Roosevelt, 1904: 69.95%
Herbert Hoover, 1928: 67.06%
Franklin Roosevelt, 1936: 66.38%
Lyndon Johnson, 1964: 61.97%
Franklin Roosevelt, 1940: 58.22%
William Howard Taft, 1908: 57.68%
Franklin Roosevelt, 1932: 57.46%
William Jennings Bryan, 1896: 56.97%

West Virginia
Abraham Lincoln, 1864: 68.24%
Lyndon Johnson, 1964: 67.94%
Richard Nixon, 1972: 63.61%
Franklin Roosevelt, 1936: 60.56%
Ulysses Grant, 1868: 58.83%
Herbert Hoover, 1928: 58.43%
Jimmy Carter, 1976: 58.07%
Harry Truman, 1948: 57.32%

Wyoming
Ronald Reagan, 1984: 70.51%
Richard Nixon, 1972: 69.01%
Theodore Roosevelt, 1904: 66.72%
Warren Harding, 1920: 64.15%
Herbert Hoover, 1928: 63.68%
Dwight Eisenhower, 1952: 62.71%
Ronald Reagan, 1980: 62.64%
Franklin Roosevelt, 1936: 60.58%

After 2000, George W. Bush's '00 vote share was in the top eight in seven states; after 2004, his '04 vote share was in the top eight in 11 states, including one state that had voted for Bill Clinton twice (Kentucky). After 2012, Romney's vote share was in the top eight in six states, including three that had voted for Bill Clinton twice (Tennessee and Kentucky, in addition to West Virginia).

I didn't look for any additional states for the last four Democratic nominees, but I did for Gore and Kerry, and didn't find any, except Hawaii, where Gore would have been #5 from 2000 until 2008, #6 from 2008 until 2012, #7 from 2012 until 2016, and #8 from 2016 until 2020. Kerry would have been #8 from 2004 until 2008, but he got 54.01%. (Gore had gotten 55.79%.) Of course, New York is a very large state.

As of October 2000, only four nominees (one of them Bill Clinton in '96) had gotten over 55.5% of the vote in Hawaii, and only five had done so in Alaska. So I think a similar exercise done at the time would have dismissed those states as too young to take into account in the same way. However, as of October 1996, only seven nominees had gotten over 55.5% of the vote in New York. However, New York and Hawaii were the only states in which Bill Clinton entered into the top eight in 1996 even at the time. So, using the same logic as on the parent post--and imagining we discounted Alaska and Hawaii due to their youth--eight would have been the significant number as of October 2000 as well (because only eight nominees would ever have gotten over 55.5% in New York, and more would have done so in every other state apart from Alaska and Hawaii).