Here's where a latin name is needed, Anne - you're thinking of planting a 'mock orange' but to me, that's a Philadelphus, which isn't a climber - it's a free standing shrub. Did you mean that? It's also deciduous.

Evergreen clematis - yes, there are some. They flower in the winter months - look at the Clematis cirrhosa group. The one that's most often seen is 'Freckles' but there are others. All lovely and worth growing. They take up about 6 - 8' of trellis each when they're mature. There's also C. armandii, but I wouldn't recomend that for a trellis - once it gets going, it's very vigorous.

Honeysuckle -there are quite a number of evergreen varieties, so that would be fine - choose a not-so-vigorous one, though, or it'll take over the trellis! One plant would also take up 6 - 8' of your space.

It looks as though you need three plants max. to cover that length. You could add a spring/early summer flowering group 2 clematis so you'd have something in flower most of the year. That would be deciduous, and only needs a trim to keep it tidy. Group 2 clems often flower twice, too! :-))