When Lieutenant Governor Paterson announced on March 13 that he would assume the duties of the governor of New York State in five days, he said he felt like the “student who’s getting ready for the final exam” but didn’t “attend any classes.” As a former lieutenant governor I felt for him.

Behind his self-deprecating comment is a lesson for all states that rely on a lieutenant governor to become a successor in the event a governor cannot serve.

Since 1900, 51 governors have died in office, and many others, from George W. Bush in Texas to John Rowland in Connecticut, have vacated office to assume a higher office, face criminal charges, quell scandal, or for other reasons. Succession is vital.

Unfortunately, it is almost always the case that governors marginalize their lieutenant governor, excluding the number two from cabinet meetings and day-to-day administration. That leaves the lieutenant governor facing the test without the necessary knowledge. Imagine corporate CEOs routinely excluding their number two from involvement or knowledge of day-to-day operations. Shareholders and the board of directors would insist on better management practices. When Nelson Rockefeller was governor of New York and campaigning for the presidency, he leaned on Lieutenant Governor Wilson to literally run the state, but that was exceptional. Lieutenant Governor Krupsak was excluded from virtually all meetings with the governor’s inner circle and was barely on speaking terms with Governor Carey.

Mario Cuomo’s first lieutenant governor, Al Delbello, quit in exasperation at having so little involvement in state matters. Mary Donahue once told the New York Times that she held onto her job as no. 2 “by doing for Mr. Pataki what a governor really wants from a lieutenant governor, praising him and staying out of the way.”

That probably is what most governors want, but the public should ask for more cooperation so that what the state constitution promises can actually occur: transition to a prepared leader.

In New York State, the lieutenant governor presides over the upper house of the legislature and has every opportunity to master pending legislation and the state budget line by line. I did, and David Paterson, who has served in the legislature for 23 years, assuredly has too.

But there are other executive matters such as the insurance department, health department, state police, prison system, etc., that a lieutenant governor needs to be informed about as well.

By the way, the same lesson applies to vice presidents. Harry Truman was sidelined during most of Franklin Delano Roosevelt’s tenure, even when the president’s health was failing.

As David McCullough relates in his Truman biography, the vice president was sitting in a Capitol office sipping whiskey and talking politics on the afternoon of April 12, 1945, when he was summoned to the White House. He was immediately ushered into Eleanor Roosevelt’s second floor study, where the first lady told him the president had died. Stunned, Truman asked the first lady if he could help her in some way. She replied, “Is there anything we can do for you, you’re the one in trouble now.”

One of the most urgent problems was that Truman lacked knowledge about national security issues when he was thrust into the presidency.

Today, gubernatorial candidates often choose a running mate for gender balance or racial or geographical diversity, and the two candidates campaign together, projecting a picture of cooperation and closeness. If they manage to win, the togetherness often comes to an abrupt halt.

The public should learn from recent events in New York. Mr. Paterson said, “I feel that I’m sitting on a sand castle that other people built.” There’s more than a grain of truth in his humble admission. State constitutions provide for succession, but it’s up to the governor to help make it successful.

Ms. McCaughey, a former lieutenant governor of New York State, is an adjunct senior fellow at the Hudson Institute.