Blinkage

[Gemini Cricket]

Here's a blinkage question:

Two cars meet at an intersection with stop signs at each crosswalk. One car is going north, the other south. They get to the stop signs at the exact same time. If there's no blinkers on the other car, I go forward. If there is, I usually wave them to go.

But...

Today, this happened to me. I went forward, the car turned towards me in the middle of the intersection. The driver wanted to make a left. No blinkage. There was honking, hand signals yaddah yaddah.

No blinkers, I'm thinking yeah he's going straight.

Or...

Is it supposed to be one at a time only crossing the intersection? Whereby I would be at fault...