Does your fence get much sun? That makes a major difference to what will produce.
Also,
should I assume you're after a
perennial vine?
From what I know, Seattle doesn't get much summer heat and the majority of fruiting/productive vines seems to be at least subtropical.
But my climate's far from tropical, and I have a very productive black passionfruit on my North-facing fence (Southern hemisphere)
The passionfruit shares with a rocoto chilli, which is perennial in temperate climates
It's not a climber, but kind of...'climb-y', gangly and sprawly, but it has gorgeous (and yummy) fruit like little
hot bell peppers, all winter long round here.
There's fun climbers like luffa and tromboncino rampicante, but they'll be annuals in your climate.
Runner beans will probably be perennial for you, but they'll die to the
roots in winter, so bare fence...
Another possibility, depending which way the fence (and your interests) lies, are
espalier and cordon fruit trees .
You can use dwarfing rootstocks, so the tree is naturally small, as well as doing some pretty brutal pruning.
It aint for everyone, but I let my espalier apples have their first crop this year, and by growing like this I can (kind of) fit in two apples, a peach, multi-grafted pear and plum.
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