"Twenty-five years later appeared the next sign mentioned in the prophecy—the darkening of the sun and moon. What rendered this more striking was the fact that the time of its fulfillment had been definitely pointed out. In the Saviour's conversation with His disciples upon Olivet, after describing the long period of trial for the church,—the 1260 years of papal persecution, concerning which He had promised that the tribulation should be shortened,—He thus mentioned certain events to precede His coming, and fixed the time when the first of these should be witnessed: “In those days, after that tribulation, the sun shall be darkened, and the moon shall not give her light.” Mark 13:24 . The 1260 days, or years, terminated in 1798. A quarter of a century earlier, persecution had almost wholly ceased. Following this persecution, according to the words of Christ, the sun was to be darkened. On the 19th of May, 1780, this prophecy was fulfilled. GC 306.1"
"But in those days, after that tribulation, the sun shall be darkened, and the moon shall not give her light,"
Ellen White directly references Mark 13:24 in this passage.
"“Almost, if not altogether alone, as the most mysterious and as yet unexplained phenomenon of its kind, ... stands the dark day of May 19, 1780,—a most unaccountable darkening of the whole visible heavens and atmosphere in New England.”—R. M. Devens, Our First Century, page 89. GC 306.2"
"The sun shall be turned into darkness, and the moon into blood, before the great and the terrible day of the Lord come."
The EGW passage describes the dark day of May 19, 1780, and the Joel passage prophesies the sun turning into darkness. The connection is that the dark day is seen as a partial fulfillment or foreshadowing of the Joel prophecy.
"An eyewitness living in Massachusetts describes the event as follows: “In the morning the sun rose clear, but was soon overcast. The clouds became lowery, and from them, black and ominous, as they soon appeared, lightning flashed, thunder rolled, and a little rain fell. Toward nine o'clock, the clouds became thinner, and assumed a brassy or coppery appearance, and earth, rocks, trees, buildings, water, and persons were changed by this strange, unearthly light. A few minutes later, a heavy black cloud spread over the entire sky except a narrow rim at the horizon, and it was as dark as it usually is at nine o'clock on a summer evening.... GC 306.3"
"The sun shall be turned into darkness, and the moon into blood, before the great and the terrible day of the Lord come."
The EGW passage describes a dark day event, which is presented as a sign of the end times. Joel 2:31 also describes cosmic disturbances (sun turned to darkness) as preceding the day of the Lord. The parallel is clear and significant.
"A day of darkness and of gloominess, a day of clouds and of thick darkness, as the morning spread upon the mountains: a great people and a strong; there hath not been ever the like, neither shall be any more after it, even to the years of many generations."
The description of the darkened sky and ominous clouds could be seen as a parallel to the descriptions of the day of the Lord in Joel 2:2.
"Travelers put up at the nearest farmhouse. ‘What is coming?’ queried every lip and heart. It seemed as if a hurricane was about to dash across the land, or as if it was the day of the consummation of all things. GC 306.4"
"Men’s hearts failing them for fear, and for looking after those things which are coming on the earth: for the powers of heaven shall be shaken."
The EGW passage describes people's fear and apprehension during the dark day, mirroring the fear and anxiety described in Luke 21:26 regarding the events leading up to Christ's return. Both passages highlight the emotional response to impending events.