Where most of us run into problems with the park brake rod hanging up is because we decided to cut the center crossmember out under the bellhousing to run a different engine and trans combo and the weight of the cab pushes down on the body mounting bracket and twists the frame rails until the cab has sagged down to where the floor supports are laying on the frame rail and pinching the brake rod where it goes over the frame.
That happened on my truck and you can see it on a lot of older builds with V8 automatic swaps that have been driven a lot when you look at them from the side and they look slightly bent at the cowl and the hood won't line up.
I thought I had an example photo but can't find it but if you stop this video 24 seconds into it where it gives a straight on side shot from the passenger side you can see that the hood doesn't flow just right and the gaps are wrong. No doubt it wasn't built that way but over time the cab has sagged because the body mounts on the frame have twisted the frame and sagged from the weight.
https://www.youtube.com/watch?v=LbC921wvUyo