@Unknownymous dude! I have never experienced this with a handshake but experience it when dancing with girls or holding there hands. I use it to create "special" moments with them by touch an it gives them the impression we can communicate without words an it drives them wild. Hang out a couple of times with girls an this touch pattern is actually a communication but that is something else entirely.
For the handshake it depends if they have always been told that ya need a firm handshake an so they squeeze in an unsocialised attempt of a firm handshake. Otherwise its to get your attention. They may politely shake hands with everyone but gives a squeeze to someone they like.
When am holding a girls hand to dance with them or lead them (I want to specify a usually do night game) an they squeeze, I squeeze lightly back. it usually leads to playing with their fingers or pulling them in. Its very hard to explain in text as its clearly a very physical method....
Look at her body language an facial expressions, if it was wide eyed an being please to meet you squeeze back. Try to flip from the "polite" handshake to take her hand. If ya going to hold it, pull her in slightly or make sure ya invading her space:
Read/watch the first reply! thanks
@Space for posting the video! It covers the handshake....