Engine won't turn off - turn signal switch?
 

Gentlemen
This afternoon I finally had a chance to check out the electrical system.
I did find something odd.
When the turn signal is used and cancels after the turn, the low beams would go off.
If I touch the turn signal switch, the lights would come on.
Both high and low beams work correctly and I use a relay setup for the headlights.
I replaced the turn signal switch with a new unit 5 months ago.
Any direction would be appreciated.

After the HVAC system, this turn signal / high beam switch is the worst engineered part of our cars.

If you take off the wheel, and remove the plastic clamshell steering column housing, you'll see the metal contactors for the high beam switch - these bend over time and don't function well. You should be able to see how to bend them back into position so the low beam switch is firmly connected.

HTH,
Chuck.H
'89 TurboLookTarga, 367k miles