Silver has voice lines about bright lights maybe helping him stave off sleep, says he keeps moving in order to keep from getting sleepy, and he has tried gum as well.
(The literal line is “bottle gum,” and is possibly a reference to caffeinated gum that comes in little plastic bottles and is advertised as a way to keep you alert when you are drowsy.)
Silver tries making a wake-up potion with Kalim and Jamil and then says he will no longer be a slave to his drowsiness, but we do not see the results of the potion to confirm whether or not it was effective.
One of the reasons Silver joins the Master Chef course is to learn tricks for maintaining focus in the face of distractions to help overcome his tendency to fall asleep everywhere.
He says that he has fallen asleep while boiling something for dinner several times before, and does almost fall asleep during the class.
At the conclusion of the course, however, we receive a rare hint that there might be a solution to his sleepiness problem: he says that he spent much of the day thinking about how he would like to make tomato-based dishes for Lilia, and those thoughts might have been enough of a distraction to keep him from falling asleep.
Silver’s sudden sleepy spells are often commented on: Ortho says that Silver fell asleep two minutes after he started telling Silver a ghost story, Jade wonders if Silver is capable of falling asleep on thrill rides, and Lilia says that he will often fall asleep while standing up.
Ace says he has heard about Silver falling asleep without warning, Grim comments on Silver falling asleep while they were decorating Ramshackle and in the school’s courtyard, and Malleus teases Silver about being awoken by the Bell of Salvation during the Glorious Masquerade event.
Malleus purchases coffee for Silver during the Firelit Sky event, saying, “it might help him stay awake,” and when speaking to a confused Idia in Book 7 he says, “you seem sleep-addled. It reminds me of Silver, from my own dorm.”
Riddle mentions a time that Silver fell asleep while changing his clothes after morning practice wit the equestrian club, saying that he and Sebek had to physically carry him to class.
Asking Silver if he is half asleep seems to be common amongst the members of Diasomnia, and Sebek in particular.
Silver says that he doesn’t become irresistibly sleepy when he is in dreams, but there may be exceptions: even within Lilia’s dream he starts to become drowsy after seeing the Dawn Knight, when his ring starts to glow.
Twisted Wonderland Reference Note 