Is NOT expected behavior w factory OEM wiring.
Likely one of 3 things in my opinion:
- intentional (to emulate some late model vehicle signal illumination behavior)
- bulb related if LEDs installed. these vehicles are pre-LED and electrical system is sensitive to having LED installed w/o proper modifications including resistors etc.
- 'issue' w wiring harness (getting a short someplace - look for cracked/melted insulation on wires in harness but if same behavior both sides seems more intentional or bulb related)
Start by pulling headlight pod. Check bulbs if LED. If not, then release harness from bracket behind and look for added jumper wire(s) there - most likely a ground. Also check for hacked ground from corner lights (may be improperly hooked to fog instead of signal light (to alternate when flashing - common mod). It does NOT sound like this vehicle had the relay hacked (i.e. a workaround to enable DRL's meeting Canadian requirements of the day).
Good luck and let us know what you find from the above for next steps