in numerous vintage cars*** I use Mobil 1 0w-40 in cold weather and above 40 F I use Mobil 1 15w-50. Plenty of zinc / phosphorus in both of them for flat tappet engines. Never had any oiling issues.
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*** I've used those oils for 15-20 years in Jaguar e types, XK-120 & 150's, MGA's, Austin...