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There are two specific design items in a cam that determine rotation.
First is the cam lobe profiles and their relationship to the crankshaft. Reversing the engine rotation requires a mirror image of the lobe relationships since you are reversing lead and lag relationships.
Second which is the real biggy is that the distributor drive gear on the camshaft needs to have a reverse pitch since it is a helical cut gear. The oil pump is only driven one direction as there are no reverse rotation oil pumps. There is also the issue that the distributor needs the cam to drive the distributor shaft up as that is how the distributor shaft bearings are designed.
There are some oddball 180deg flat cranks out there that also require an oddball cam to match. These really are racing engine parts and I would hope is not what your new engine has.