Ignition is off key light flashing, turn key on and bike still starts, turn off key light starts flashing again.

Takes the master key to get it started again. The security gives you 3 tries to get the vehicle started, after the third time, it kills the starter.
2002 Chrysler PT Cruiser Note: You must have two valid keys to add a new key to the system.
1. Insert the first valid key into the ignition switch. Turn the ignition switch to the
ON/RUN position for at least three seconds, but no longer than 15 seconds.
Then, Turn the ignition switch to the LOCK position and remove the first key.
2. Insert the second valid key into the ignition switch. Turn the ignition switch to
the ON/RUN position within 15 seconds. After 10 seconds, a chime will sound.
In addition, the Vehicle Security Light will begin to flash. Turn the ignition switch
to the LOCK position and remove the second key.
3. Insert the new key into the ignition switch. Turn the ignition switch to the
ON/RUN position.within 60 seconds. After 10 seconds, a single chime will
sound. In addition, the Vehicle Security Light will stop flashing. To indicate that
programming is complete, the Vehicle Security Light will turn on again for
seconds and then turn off.
The new key is now programmed. The Remote Keyless Entry transmitter will
also be programmed during this procedure.
Repeat this procedure to program up to eight keys.

It could be the link from the starter button to the ignition coil. If you can check this for a current it should give an indication of the problem.

If the security light is hot or flashing when the key is in the on position, most likely the ignition key tumbler housing has failed.

You can try resetting the pass code by turning the ignition switch to the on position (do not crank or start the engine). Leave the key in the on position for 10 minutes. Turn the key to the off position, wait 5 seconds and turn the key to the on position again and leave it on for 10 more minutes. Cycle the key to the off position again for 5 seconds the back on for a final 10 minutes. Once the final 10 minutes is complete, turn to the off position again, wait 5 seconds and now turn the ignition on and to the start position. The pass code has now been reset and it should start. If the reset does not work you will have to change the ignition key tumbler housing that contains the key code resistor.
Good luck

THERE IS A CHIP IN THE KEY I BELIEVE. THERE IS A RELEARN PROCEDURE YOU CAN TRY IF WHEN YOU TRY AND START IT THE SECURITY LIGHT FLASHES. HOOK UP A BATTERY CHARGER. TURN THE KEY ON AND TRY AND START THE CAR AND RELEASE . DO NOT TURN KEY OFF LEAVE IT IN THE RUN POSITION. AFTER 10 MINS THE LIGHT WILL STOP FLASHING. TURN KEY OFF. TRY AND RESTART CAR AND AGAIN DO NOT TURN KEY OFF LEAVE IN THE RUN POSITION. LET SET 10 MINS AGAIN. LIGHT WILL STOP FLASHING AFTER THAT 10 MINS. DO IT AGAIN FOR THE 3RD TIME. SHUT KEY OFF LET SET 5 SECONDS AND START THE VEHICLE. HOPE THIS HELPS

The usual reasons the fob doesn't disarm the security system is:
1) a damaged fob
2) discharged fob battery (Panasonic 2032 or equivalent)
3)electromagnetic interference
a. verify the fob in not in a metal enclosure or within 3" of any other electronic device.
b. place the fob on the seat, start motor and return fob to pocket.
c. move the bike at least 15' from the spot of interference.
With the Fob near the bike, try disabling the security system.

You'll need the PIN number.
If you don't know it, you'll have to change it to a 5 digit PIN number you select.

With the fob present, turn IGN switch:
IGNITION-OFF-IGNITION-OFF-IGNITION
Press LEFT turn signal switch 3 TIMES
Press RIGHT turn signal switch 1 TIME and release
Turn signals will flash 3 times. Current PIN will appear in odometer. The first digit will be flashing.

If changing PIN, enter first digit (a) of new PIN by pressing LEFT signal switch (a) time(s) i.e., for the number 1, press one time. for the number 5, press 5 times.

Press RIGHT signal switch 1 TIME and release.
the new digit (a) will replace the current in odometer window.

Enter second digit (b) with LEFT signal switch.

Repeat until PIN is set.

Once PIN is set (either new or old PIN), to disarm security system, DO NOT sit on seat, lift bike off kick stand, or anything else that will activate the security mode!

Turn IGN to IGNITION.

Quickly (within 2 seconds) hold BOTH turn signal switches until confirmation signal (KEY icon flashes at fast rate, in odometer window, a flashing "-" will be followed by 4 more dashes = "----")

Enter 1st digit (a) in PIN by pressing LEFT turn signal switch (a) times (i.e., 5 times for the number 5)
The 1st "-" will become the 1st digit (i.e., "5")

Press RIGHT switch signal 1 TIME.
The 1st digit is stored and the dash will flash.

Enter 2nd digit (b), and repeat sequence until done.

After the 5th digit is entered, the KEY icon stops blinking, and the system is disarmed.

The system will stay off until the IGN switch is turned off.

If at any time during disarming sequence an error is made, wait 2 minutes before trying again.

If you have a factory security system with the sensors located inside the key fobs you probably need to replace your fob battery.

System operation
System arms 5 seconds after switching ignition OFF. Switch ignition ON. Ensure clock LED illuminates for 3-5 seconds. If LED flashes rapidly at regular intervals for approximately 1 minute, then flashes at irregular intervals: Key code not recognised. Remove key and try again.
Programming
When
System malfunction: LED illuminates for 1 minute, then flashes at irregular intervals. Key(s) added or replaced.
NOTE: Replacement keys MUST have blue mark. Keys with red mark are NOT compatible with this system.
How
NOTE: Programming method using vehicle keys can be deactivated using diagnostic equipment.
Obtain 2 programmed keys (A and B). Insert key A into ignition switch. Turn ignition switch to position II. Wait 1 second. Switch ignition OFF. Remove key A. Insert key B into ignition switch within 5 seconds. Turn ignition switch to position II. Wait 1 second. Switch ignition OFF. Remove key B. Within 10 seconds: Insert key to be programmed into ignition switch. Turn ignition switch to position II. Wait 4 seconds. Switch ignition OFF. Wait 5 seconds. Start engine. If engine does not start and clock LED flashes: Switch ignition ON. Wait at least 20 seconds. Switch ignition OFF. Repeat programming procedure. Repeat above procedure to program remaining keys. Keys can also be programmed using diagnostic equipment

Press and hold the button until it flashes.

I’m happy to assist further over the phone at https://www.6ya.com/expert/robert_5bac37c3cb991fdb

The theft light issue is a good observation. Have you replaced the key tumbler or an ignition component lately? Has there been a lightning storm close very recently?

What the flashing security light is indicating is an attempt to relearn the key you are using.
Turn the key to run position, allow light to flash for 10 minutes, when light stops flashing turn ignition to OFF position for 5 seconds, turn ignition to run position and start over. Do this for 3 consecutive cycles, the the theft system will relearn the key cylinder code and store it once again.
Try that first before you go any further.
Let me know what you find.
Regards,

Theft light on indicates a problem with passlock. You have a problem with the key or ignition switch. When I worked I replaced a lot of ignition switches, so i would say that would be your problem.

Give this a try it might work for you........
When you put the key in ignition, turn it on (not to crank) dos the security light start flashing? If so, you need to either wait 15 minutes or wait with the key on until it stops flashing. Once it stops flashing, try to start again. You should get to try it 2 times before the passlock will lock up again.