I play the game of what kind of car is it when watching old movies.

This one stumped me. First I saw it as Eddie's car on Leave it to Beaver but then it popped up again.

I don't have a good picture of the whole car but the two distinctive things are the grill along the edge of the hood and the headlight buckets molded into a bullet intersecting the fender. It also has a small bullet turn signal next to the headlight.

Any ideas?