Gallicas, hybrid Gallica in this case, can grow in shade but you will get better bloom in a sunny location. IDK about this one, but my Charles de Mills blooms after the partly overhanging sycamore tree has begun to leaf out.

New Dawn is an outstanding climber...no disease and good repeat. It is also quite shade tolerant. It's flexible canes are easy to train. If you want a better flower, there is a sport of New Dawn called Awakening. Mine took a year before they flowered, but they are worth the wait. Completely hardy in my garden. Be warned, however, that they get big very quickly.

One rose that blooms like mad all summer with only half a days sun is Abraham Darby. It can be grown as a small climber (8ft) and has a fragrance to die for. It does get blackspot, but it still never stops flowering. It has had very little dieback during the winter.

My favorite climbing rose has to be Westerland or its sport, Autumn Sunset. Both bloom very well, and have been completely disease free for me in Pennsylvania (blackspot heaven). Westerland also has a great fragrance (Autumn Sunset is not as fragrant to my nose). I have heard reports that they are shade tolerant, but I have never grown them under such conditions. In my zone 6 garden, they can lose a few canes during the winter, but come back very quickly. In colder zones, they might not grow well as climbers.

Other roses you may check out are Bubble Bath and Darlow's Enigma. They are climbers/shrubs and are supposed to be among the most shade tolerant of all roses and bloom non-stop. They are on my want list to purchase, but I have not personally grown them.

Hope this helps.