One of the bread and butter techniques to attack from side control is the Kimura lock. When that attack fails because of a strong defensive grip by your opponent, my favorite follow-up attack is the “Pillow Choke”.
The best jiu-jitsu is simple. The Pillow Choke is a simple but effective strangle to be used when you can’t break the belt grip and use the opponent’s lapel to tie up their hand. It’s called the “Pillow” Choke because of the wedge you place using your knee under the opponent’s head.
With the opponent’s concentration on protecting their arm from the Kimura threat, you can use the distraction to get the collar grip that you need to apply the choke.
The Pillow Choke might be considered a variation of the Paper Cutter choke with a different grip with the second hand.
This video is from a packed Kimura seminar I did at Clark Outsourcing JIBOA jiu-jitsu in Angeles City, Philippines.