Jane, I just deadheaded two climbers this week (Climbing Iceberg) that are on trellises, and was told to deadhead the opposite of what we normally do on a rose bush: instead just above an outward facing bud, to clip an inward or downward facing bud so the growth will growing toward the trellis and not away from it. I guess the same would be true if you are growing it toward and onto a fence.
Your DJ climber is beautiful! I bought one this spring and it's in a 10 gallon pot and I haven't decided yet where it will be permanently. but am enjoying the few dk. red roses that have bloomed.