Door locks cycling, and dashboard trouble lights flashing while driving

There is something called a BSI or BCM in those cars that tends to fail. The BSI is a computer that controls all those functions. Since I am not sure where you are located, use a search engine and put in the year, make and model and the term BSI or BCM and look at the results.

The explanation could be that the Door locks are all set or
one of the door is not locked properly.

Does this vehicle have an aftermarket alarm?

that sounds like the central locking controlling lock is malfunctioning , if it is the drivers door then that lock is the control lock and need replacing

Battery Constant 12v+ Positive Wire (+): Black/Yellow
Battery Constant 12v+ Positive Wire Location: Ignition Switch Harness

Starter Positive Wire (+): Blue/Red
Starter Positive Wire Location: Ignition Switch Harness

Ignition Positive Wire (+): Red
Ignition Positive Wire Location: Ignition Switch Harness

Accessory Positive Wire (+): Red/Yellow
Accessory Positive Wire Location: Ignition Switch Harness

Parking Light Positive Wire (+): Red
Parking Light Positive Wire Location: Low In Drivers Kick Panel

Power Door Lock Negative Wire (-): Add Actuator. This vehicle uses a central door locking system. When connecting a keyless entry, you will need to add a door lock actuator and some units will also require (2) extra relays.
Power Door Lock Negative Wire Location: To Drivers Door Only

Power Door Unlock Negative Wire (-): Add Actuator. This vehicle uses a central door locking system. When connecting a keyless entry, you will need to add a door lock actuator and some units will also require (2) extra relays.
Power Door Unlock Negative Wire Location: To Drivers Door Only

Door Trigger Negative Wire (-): Red/White
Door Trigger Negative Wire Location: In Black Plug, Above Hood Release

Domelight Supervision Wire: Use Door Trigger, Requires Relay
Domelight Supervision Wire Location: N/A

Horn Negative Wire (-): Red/Green
Horn Negative Wire Location: At Steering Column Harness

Tachometer Wire Negative Wire (-): Black/Blue
Tachometer Wire Negative Wire Location: At ECM, Under Drivers Side Dash

Brake Light Positive Wire (+): White/Black
Brake Light Positive Wire Location: At Switch Above Brake Pedal

CODE ALARM SYSTEM

Used on:
Impreza 1996-2001
Legacy 1995-1999
Forester 1998-2000

Battery GP-23A

Lock: Left button will lock all doors. Double chirp indicates locked.
Unlock: Right button will unlock driver's door only. Hold unlock button app 6 seconds, it will unlock all doors including rear gate. Single chirp indicated unlock.
If the car chirps or lights flash 4x the alarm was triggered.
Panic. Press both buttons to activate emergency honk and flashing lights.
Valet mode: With optional alarm onlyPress the red alarm button on the left of the steering wheel. The light will quickly double flash. To re-set back to normal mode, press the red alarm light button again

Battery failed and lights flashing?
Parking lights will flash when the vehicle's battery is disconnected and reconnected.
To stop lights from flashing, either:
Press remote transmitter "UNLOCK" button once OR turn the ignition switch to the "ON" position and press programming button for one second (see below).
The vehicle interior (courtesy) light and door open warning light (DOOR AJAR indicator) will then illuminate for 60 seconds when the ignition is turned off, or until the doors are locked with the remote transmitter. Yes, the dashboard instrument panel lights will flash when the parking lights flash.

Programming or Overriding the Alarm when you have lost the remote
Open driver's door.
Turn ignition key to 'On'
Press and *hold programming button* in (see diagram, button under dashboard)
After 15 seconds the the door locks will cycle 3 times. Do not release Programming button.
Press lock (left) button the remotes to be programmed. The door locks will cycle one time. Exit programming mode by releasing Programming button under dashboard and turning key to off.

Code Alarm Programming Button is under dashboard on the kick panel by the driver's left knee, left of the steering column. If you can't find it, it might still be tucked up in the wiring harness higher up in that same general area. The botton is recessed in a plastic ring (see diagram).
This button must be pressed while programming remotes or if the battery was disconnected and the lights are flashing.

Trunk/doors senser locked at fault or either one is not closed / locked correctly, is your fuel cap lid also on the same sensor ?

You have a bare wire that is rubbing. Take to your local dealership.

you have a broken wire in door to body wiring loom repair this and all will be back to normal

The vehicle is preparing to set security active. It should stop blinking after 20 to 60 seconds.
Let me know.
Regards,

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CODE ALARM SYSTEM
information is always subject to change and correction Used on:
Impreza 1996-2001
Legacy 1995-1999
Forester 1998-2000
Battery GP-23A
Lock: Left button will lock all doors. Double chirp indicates locked.
Unlock: Right button will unlock driver's door only. Hold unlock button app 6 seconds, it will unlock all doors including rear gate. Single chirp indicated unlock.
If the car chirps or lights flash 4x the alarm was triggered.
Panic. Press both buttons to activate emergency honk and flashing lights.
Valet mode: With optional alarm only Press the red alarm button on the left of the steering wheel. The light will quickly double flash. To re-set back to normal mode, press the red alarm light button again

Battery failed and lights flashing?
Parking lights will flash when the vehicle's battery is disconnected and reconnected.
To stop lights from flashing, either:
Press remote transmitter “UNLOCK” button once OR turn the ignition switch to the “ON” position and press programming button for one second (see below).
The vehicle interior (courtesy) light and door open warning light (DOOR AJAR indicator) will then illuminate for 60 seconds when the ignition is turned off, or until the doors are locked with the remote transmitter. Yes, the dashboard instrument panel lights will flash when the parking lights flash.
Programming or Overriding the Alarm when you have lost the remote
Open driver's door.
Turn ignition key to 'On'
Press and *hold programming button* in (see diagram, button under dashboard)
After 15 seconds the the door locks will cycle 3 times. Do not release Programming button
Press lock (left) button the remotes to be programmed. The door locks will cycle one time.
Exit programming mode by releasing Programming button under dashboard and turning key to off.

Code Alarm Programming Button is under dashboard on the kick panel by the driver's left knee, left of the steering column. If you can't find it, it might still be tucked up in the wiring harness higher up in that same general area. The botton is recessed in a plastic ring (see diagram).
This button must be pressed while programming remotes or if the battery was disconnected and the lights are flashing.
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