Park Not Disengaging and Reverse Engaging at Same Time?

Before I stripped the '65 Formula S, when I engaged reverse with the floor shift, oftentimes I could hear the clickety, clickety, click noise of the transmission park mechanism not fulling releasing as I backed up. When I put things back together, I hope that problem does not persist. I assume it is a cable adjustment glitch of some kind. Anyone else experience this? Thank you.

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