Piper Aztec Pilot reported the nose landing gear collapsed during landing rollout.

Narrative

I was coming into land at ZZZ on Runway XY. I went through the descent and before landing checklist as well as GUMPS Airspeed 95 kts.; stable descent - two red two white. I had 20 degrees of flaps in; I verified three different times landing gear was down and locked - three green and one in the mirror. I touched down the main gear first; smooth touchdown. As I let the nose down gently there was a violent shake from the nose gear so I immediately pulled aft on the yoke and kept the nose gear off the ground for as long as possible. As airspeed decreased; the nose eventually set back down on the Runway on its own and the nose gear started to shake again and progressively got worse until it eventually collapsed. At that point I immediately [advised ATC]; shut the engines off; secured the cockpit and exited the aircraft. After examination of the aircraft I noticed the scissor pin connected through the stationary portion of the scissor gear but the scissor portion was not connected. I recall verifying the pin was inserted during preflight but suspect that I missed verification that the pin was through the scissor portion of the gear. I always considered my preflight inspections to be thorough and will take action to increase my awareness to better improve my preflight inspections moving forward.