First, any Avatar can go into the Avatar state. Only a fully realized Avatar can control it. Otherwise, it's a defense mechanism.
He regularly got pushed into the defensive Avatar State. During the escape from Ba Sing Se, Aang realizes what Guru Pathik was teaching him, let's go of his earthly attachments (Katara, much like Zaheer did when P'Li died), and while in control of the Avatar state, gets attacked by Azula. The Avatar state gets locked away when he dies, and gets resurrected by the Moon water Katara had. Most of the final season, it can't be used. It's only at the very end during the Phoenix King attack, that being hit on the same spot as where Azula hit him, that it's unlocked again, at which point Aang can control it again.
Philosophically, once you reach enlightenment, and let go, you let go. You are no longer in the state of mind to reattach and regain the earthly attachments. Aang lived the rest of his life in a very Buddhist/Zen state.
As for her, we get the quote from Roku in The Last Air Bender, that the glowing lights are the power of the previous lives of the Avatar.
The Avatar State is a defense mechanism, designed to empower you with the skills and knowledge of all the past Avatars. The glow is the combination of all your past lives, focusing their energy through your body.
This was an amazing plot detail, that Legend of Korra quickly, and disrespectfully retconned, when
the giant space bacteria Raava, Vaatu, and Wan were introduced. Further backed up by Unalaq's merging.
Wan, the first time he channels Raava, before they merged completely.
Avatar Wan, the first Avatar, in the true Avatar State.
Notice Wan, with only Raava and the power of the Harmonic Convergence, is in the completely realized Avatar State glow. No past lives. Notice Unalaq, merged with Vaatu, also in a anti-Avatar glow. No past lives.
Notice Raava and Vaatu's natural state. The same exact glows.
Of course, at this point, Korra still had her past lives. It's only once Raava is ripped from her, that the connection to the previous Avatars is removed. Afterwards, she regains Raava, but not the past lives.
This means one thing. The Avatar State, and Glow, are completely due to Raava's merging and power to hold multiple elements, while the Past Lives have nothing to do with it.
It's a mere pleasant coincidence that the Avatar State allows for a direct connection with past lives, but the power comes just from Raava.
Thanks for ruining the nicely established lore Korra, thanks a lot.
Of course, in universe, the explanation given is that much of the Avatar's history is unknown, lost within the ages. The Avatars' are all seen to communicate with their predecessors, Korra to Aang, Aang to Roku, Roku to Kyoshi, etc, instead of with Wan. They don't even know about Raava or Vaatu. It's only during Season 2 of Legend of Korra that she learns about Raava and Wan, reintroducing them to the truth of the Avatar, and the Avatar State. So chalk it up to a game of telephone, knowledge that changes through the years after multiple retellings. Roku just spit out what he learned, even if it was wrong.