Entry tags:
Timeline and cutscene references
(Work in progress, spoilers follow)
Link to ENG cutscene compilation: Patch 4.x - 5.0
Link to JPN cutscenes: Patch 4.x | Patch 5.0
A REALM REBORN
+ Tendrils of Intrigue, Scene #?
(War of succession ends and Varis takes the throne from his uncle)
STORMBLOOD
+ Prelude in Violet, Scene #3
(First reveal as Solus zos Galvus, woken to clean up Lahabrea's mess)
+ Seiryu's Wall, Scene #2
(Realisation that Black Rose possesses the 'perfect aspect')
+ A Requiem for Heroes, Scene #8
(Mentioned in passing by Elidibus-as-Zenos and Varis)
SHADOWBRINGERS
+ Emergent Splendour, Scene #
(First glimpse on the First, watching Vauthry's fit over Alphinaud's insult)
+ The Oracle of Light, Scene #2
(Watching the battle with Ran'jit)
+ The Wheel Turns, Scene #1
(First approach at the Crystarium, after Titania's defeat)
+ A Party Soon Divided
(Meeting in the Oracular the morning after)
+ Into the Dark, Scene #1 and #2
(Entering the Rak'tika Greatwood)
+ In Good Faith, Scene #1 and #2
(Apprehended by Viis, after Y'shtola falls)
+ The Burden of Knowledge
(After Qitana Ravel)
+ The Best Way Out
(In the Ocular, before Amh Aereng)
+ Have a Heart
(Conversation with Exarch during Talos revival)
+ Return to Eulmore
(In the Ocular, speaking on the nature of sundering)
+ The View from Above
(Rebuilding the Ladder)
+ Extinguishing the Last Light, Scene #6 and 7
(#6: [echo] Emet-Selch creates Vauthry; #7: After Mt Gulg)
+ A Greater Purpose
(Hythlodaeus at the Bureau of the Secretariat)
+ Shadowbringers
ENDWALKER
(See lvl 86-67 MSQ)
(See also: narration for entry into each zone)
+ Endwalker (MSQ)
Calamities
Fifth shard: wind
Twelfth shard: lightning
Second shard: fire
Third shard: earth
Sixth shard: ice
Tenth shard: water
Seventh shard: darkness
Link to ENG cutscene compilation: Patch 4.x - 5.0
Link to JPN cutscenes: Patch 4.x | Patch 5.0
A REALM REBORN
+ Tendrils of Intrigue, Scene #?
(War of succession ends and Varis takes the throne from his uncle)
STORMBLOOD
+ Prelude in Violet, Scene #3
(First reveal as Solus zos Galvus, woken to clean up Lahabrea's mess)
+ Seiryu's Wall, Scene #2
(Realisation that Black Rose possesses the 'perfect aspect')
+ A Requiem for Heroes, Scene #8
(Mentioned in passing by Elidibus-as-Zenos and Varis)
SHADOWBRINGERS
+ Emergent Splendour, Scene #
(First glimpse on the First, watching Vauthry's fit over Alphinaud's insult)
+ The Oracle of Light, Scene #2
(Watching the battle with Ran'jit)
+ The Wheel Turns, Scene #1
(First approach at the Crystarium, after Titania's defeat)
+ A Party Soon Divided
(Meeting in the Oracular the morning after)
+ Into the Dark, Scene #1 and #2
(Entering the Rak'tika Greatwood)
+ In Good Faith, Scene #1 and #2
(Apprehended by Viis, after Y'shtola falls)
+ The Burden of Knowledge
(After Qitana Ravel)
+ The Best Way Out
(In the Ocular, before Amh Aereng)
+ Have a Heart
(Conversation with Exarch during Talos revival)
+ Return to Eulmore
(In the Ocular, speaking on the nature of sundering)
+ The View from Above
(Rebuilding the Ladder)
+ Extinguishing the Last Light, Scene #6 and 7
(#6: [echo] Emet-Selch creates Vauthry; #7: After Mt Gulg)
+ A Greater Purpose
(Hythlodaeus at the Bureau of the Secretariat)
+ Shadowbringers
ENDWALKER
(See lvl 86-67 MSQ)
(See also: narration for entry into each zone)
+ Endwalker (MSQ)
Calamities
Fifth shard: wind
Twelfth shard: lightning
Second shard: fire
Third shard: earth
Sixth shard: ice
Tenth shard: water
Seventh shard: darkness

SOLUS ZOS GALVUS
A family tree, based off Tales from the Dawn: A Question of Death. (Original source)
Solus was born in 1489, joined the military at age 16, and became legatus at the age of 24, in 1513. In 1517, he was granted control of Garlemald as dictator by popular vote.
(Died at the age of 88.)
Varis: died at age 46
Zenos: died at age 26
Solus' estimated age at birth of his first son, Lucius: 22
At the very least, Lucius CANNOT have been born after he became emperor as then Lucius would be only 14 at the birth of Varis; at the earliest, he would have been born after Solus became a legatus, which would make Lucius 18 when Varis was born. However, given the trend, it's far more likely he was ~20 and therefore was born before Solus attained the rank of legatus.