This original poster's rose is a typical hybrid tea with single blooms on long stems, not a climber like Joseph's Coat with multiple blooms on short stems branching off long arching canes. This is an older photo of my Joseph's Coat climbing up the left side of the garden gate, which has a ceramic tile placed in the center of it.
When trying to identify an unknown rose, it helps to look at the form, shape and structure of a rose (as well as its leaves), not just the color of its blooms.