What liquid primer would you recommend?

Easiest way to determine is there is any enamel based primer or paint is to take a small aerosol can of spray lacquer and shoot a few spots with it.
Sit back and wait a bit. If it is enamel the lacquer will start ruining itself and turn into a wrinkle finish.

I generally shoot acrylic enamel with hardener added. Most of my work has been on motorcycles and it holds up very well even being subjected to oil and gasoline.

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Thanks. I think my problem spots are flexible. I’ve found additives to make paint flexible and a YouTube video showing how well they work, but they come in large quantities, aimed at professionals. I’d think a hardener would exacerbate this.

I think your adhesion problem is due to the cowl panel being galvanized.