Welcome to the forum!
I hope you have (or can borrow) a voltmeter, because we're going to have to make some measurements.
First, I suggest you download the service manual (free, in the stickies at top of the 660 Maintenance section). The last page is the wiring diagram. Use it to follow and understand what we're doing.
OK - to get the starter to turn over you need a few things to happen:
(All measurements are taken with meter set to DC voltage, if not auto DC then 20VDC, black probe on battery minus, red probe takes measurement)
1) in neutral - is your green neutral light lit? This also proves that the key switch is on and that voltage is getting to at least some of the electrics.
2) with meter probe on the solenoid's positive battery cable connection (where the cable from battery + is bolted to solenoid) is there ~12V here? Now press the start button - is there STILL ~12V here - should be. If voltage drops below 10V or so, the battery, cable or cable connection/s are bad.
3) does the red/black wire at the CDI have ~12V on it? Now press the start button - still has ~12V on it? It should. You can take a straight pin and pierce the insulation around the wire - make sure the pin is into and through the copper strands, then put your meter probe on the pin.
4) Use the pin again. Does the yellow black wire at the solenoid have 12V on it?
5) Does the yellow/black STAY at around 12V when you press the start button? It should. IF not we can deal with it, but need to know.
6) While you're pressing the start button does the red overtemp light illuminate?
7) Use pin again - Does the blue/black wire at the solenoid have ~12V on it UNTIL you press the start button, then it goes to low V (0-1V or so) while pressing the start button?
Most likely, your tests will fail somewhere between 1 and 7. Let us know the results.
ALSO - you may, at some point think "Ahaaa, if I jump 12V to the yellow black at the solenoid, all will work!"... DON'T DO IT! If the yellow black is still connected to the CDI when you jump 12V to this wire, you will damage a transistor inside the CDI!
Let us know what you find and good luck. We'll deal with the 5 second issue after you get the starter working.
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'01 Polaris Scrambler 400, K&N
'02 Honda 400ex, Big Gun pipe, jetted, K&N, Lonestar +2 A-arms, Lonestar anti-vibe
'04 Suzuki LTZ400
'16 RZR XP4 1000 Turbo
Last edited by QuadManiac; 11-10-2017 at 02:16 PM.