Chrysler Repair: 99 LHS 3rd Time is a Charm, solenoid switch, switch points

Question
Hi Roland,
What would cause the starter not to engauge until the third try?
Try #1 - Turn key to start, no click heard, just like perhaps a bad solenoid.  So turn ignition to off position.
Try #2 - Same thing as try #1.
Try #3 - Cranks right up.
Battery is in good condition and car runs great.  But been doing this for over a year now.  Not 1st or 2nd try, but always 3rd try.  Why?  
Thanks Mike

Answer
Hi Mike,
I can't imagine why a pattern like that but you could probably test it since it is so predictable. It has to either be the ignition switch, the relay (in the box under the hood), or the solenoid switch on the starter. The place to start is the relay where you should see 12v on the rear most pin (of the three side-by-side) when you turn the key to start. If not, then the ignition switch is flaky.  If you get that, then the relay should click when replaced in the socket on the first try. If it doesn't and only clicks on the third try, then the relay is bad. If the relay clicks reliably then check to see if 12v appears on the light green wire at the starter motor when the relay clicks or look at the middle pin {the true middle, not the middle of the three} of relay socket if you can sneak a small wire in the pin socket and route it out for testing. If it doesn't the switch points inside the relay are no good. If it does then the solenoid switch of the starter is no good.
Roland