In his book, The Battle of Seven Pines, Smith says "The next morning (June 2), I was compelled by illness to leave the field." Morning is not very specific.
Govan and Livingwood in their Johnston biography, A Different Valor, put Lee's assumption of command at 2:00 pm June 1, the latest time I've seen from pop historians. This 18 hour remark would move out to an 8 a.m. June 2 recovery. Their time is not sourced. However...
In the Battle of Seven Pines, Smith talks of Lee's assumption of command this way:
About 1:30 pm. [June 1st] President Davis rode up and asked for General Lee. On being told that I had not seen General Lee during the day, the President expressed so much surprise that I asked him if he had any special reason for supposing General Lee would be there. To this he replied ; Yes; and added that early in the morning he had ordered General Lee to take command of the army at once. [...] General Lee arrived at about 2:00 p.m. and at once took command of the army.What he means is formal command, for he adds, "General Lee made no adverse comment on my management of the army and gave me no orders then or any other time that day."
Between 4:00 pm and 5:00 p.m., Smith and Lee are riding on the Williamsburg Road. They encounter Longstreet who renders a report to Smith; Smith redirects the report to Lee. At 6:00 p.m. they return to Smith's HQ and Smith issues orders recalling troops sent to Longstreet's aid. Smith is fully himself into the evening.
So a June 2nd recovery is consistent with a June 2nd affliction, but the details are difficult.
One of Harry Smeltzer's readers wrote him to say:
“Glatthaar, OTOH, says Smith had suffered the 'paralysis' before the war, when he was street commissioner in New York City." “A bout with paralysis forced him south for treatment. The Federal government misconstrued his intentions and deemed him an enemy, so Smith offered his services to the Confederacy.”It is dangerous to rely on Glatthaar for anything. Only the paralysis matches Smith's obituary which puts it this way:
After the election he continued attending to the duties of Commissioner, and served out the term for which he had been elected. His administration of the office had been very able and honest, and had given great satisfaction. He held over, awaiting with anxiety the appointment of a successor. Owing to overwork, about two weeks before active hostilities actually began at Fort Sumter, Charleston, Captain Smith was struck down by paralysis and confined closely to his room for some months. When recovered sufficiently, he went to his friends in Kentucky. At a later day he learned it was the intention of the U. S. authorities at Washington to arrest and imprison him, and he proceeded to Richmond, Va., in September. About this time he resigned the office of Street Commissioner of New York City.Steven Newton in Joseph E. Johnston and the Defense of Richmond, writes of the famous Richmond war conference involving Davis, Lee, Johnston, Longstreet, Smith, and Randolph,
Smith he finally located at the Spottswood Hotel only thirty minutes before the appointed time. There, his second in command had nearly collapsed from the exertions of the previous few days and his chronic nervous malady. Smith told Johnston that he felt entirely too ill to participate...The citation for this vingnette is excellent, an unpublished account of a conversation between Smith and Bevery Bohnston (Joe's brother) in 1863.
Worth looking into: conversion disorder and Jean-Martin Charcot.