Hello and welcome to AP - you'll find lots of info and help here.
Looks like an end of stroke problem to me.
I've put some numbers on you picture, to describe what should be happening. What should happen is when flipper plunger 1 pulls in the cam 2 swings around and hits the switch leaf 3. You correctly observe that 3 should have the little plastic cone on it. This cone then hits 4 - the outer bit of the switch and makes a gap between 4 and contact 5. This gap should be about two to three mm when the flipper is engaged.
if you've got the cone bit i'd try and glue it back on - superglue or the non acicidc silastic may work.
