Uncertain rose - pruning

[YesILikeItToo]

I have this rose, which was really tall and lying across the whole border when I moved in, I've been cutting it back. A gardener who gave me some advice thought it might grow up and over a frame, but it hasn't shown any desire to 'tumble' since i cut it down, it just grows straight up each year. The RHS website suggests pruning in March and then looking for clues as to what sort of rose it is over the summer. I've gone out to do this, but I'm unsure now - all the buds and stuff are right at the top on the red bits should I be cutting right back below the red bits again into the green?

It looks thornless so that will reduce the possible list of contenders right away. Its habit is probably a climber so IIWM I would just let it do it's thing this summer and you should have your answer. No need to prune unless you don't like its size, although I imagine it will appreciate some more sturdy upright support so I would move those canes to vertical at this stage.

Most roses are pruned in spring, to give growth to the strongest shoots, by removing the weaker ones. Your rose looks like a thornless climber. Go back to the RHS website and search 'thornless climbing rose' . You might then be able to identify it from the roses that appeared last year.
Climbing roses send shoots out from the horizontal stems. That's why you've got a whole lot of verticals from that large horizontal. A trellis style framework will stabilise the rose and allow you to prune to a loose fan shape. After prune give the rose a feed with rise fertiliser.

I would never have thought to fertilise it, Glad you think it's worth it!

Thanks both for the 'thornless' insight - another clue.