I have the same problem. I cleaned the contacts replaced the starter and sometimes I get crank-stop-crank-stop Need to check immo, relay?
This is very similar to a dead battery, because if i connect charger on 1 minutes or less, the car starts perfectly! but i have new battery It seems that somewhere the voltage drops and some kind of relay does not work. help))
Have you performed a voltage drop test on the starting system ? There are multiple links on google "how to do voltage drop test on starting system".
After replacing lots of wire harnesses and running down various rabbit holes, it was narrowed down to a defective immobilizer. There appears to be a lot of 360, CS, 355, 430, 550, 575 and 612s with bad immo's as well. Because I am in AZ and I am no stranger to a race traci, I may be generating more heat, and mine was an early failure. The immobilizers in our cars are garbage and meant for cars that usually end up in the junk yard in less than 10 years, not Ferraris that are loved and cared for, for generations. Ferrari's fix....... new immobilizer, fobs AND engine ECUs, to the tune of $15K. It doesn't address the core issue of the immobilizer being junk. It just sets the car up for another failure. I started working with 360Trev who is a genius on the computer and electronic side. Long story short.... he reverse engineered the enginev ECUs to eliminate the immobilizer in the code. The car no longer looks for the signal that it's OK to start. Result...... starts every time. Problem solved! This journey had lead Trevor to develop a tool for our cars called the 'Swiss Army Knife'. As far as all the functions he has developed, you will have to speak with him.
Been there and done that. It is just a patch and doesn't address the cause. If you talk to Specialized, a prerequisite for this is a properly functioning immobilizer system. The only real long term solution is to make the immobilizer a non issue.