Already, when you say press-on 1/24 that kind of limits the field... The wire wheels look a bit like the fronts on the Eldon 1/24 dragster, but those were skinnier, and the back wheels on this car don't look like either of the two others you show here. I think Strombecker also made some press-on wire wheels, but those would be in 1/32 or more likely 1/30 scale.
I believe Eldon made some other cars between 1/32 and 1/24 scales which might have press-on wheels, so that might be the likeliest candidate. Mostly Indy cars.
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