I read Hagerty's policy a little differently (I have three antique vehicles covered by them):
https://www.hagerty.com/insurance/classic-car-insurance/does-my-vehicle-qualify

There is no direct linkage to another policy, you just have to another regular-use vehicle that has insurance.

"Regular-Use Vehicles
All household members with a valid driver’s license must have a regular-use vehicle for daily driving.
(Motorcycles and public transportation are not considered viable regular-use vehicles by our program in most cases. Contact us for details).
Applicants must also maintain regular-use insurance in their own names."


Original question/post:
"Does anyone know of a company that will insure an older vehicle(pre-1960) without requiring you to have a late model with regular insurance?"

You do not need a "late model", but you need another daily driver vehicle with regular insurance.