Not to be a nitpicker, but if you have one "exactly" like that - it's not an EA-260 (which I have). That's actually a 5120e; the model
before the EA-260, which replaced the 5120e's in, IIRC, 1971. No real difference, though; other than different pickup trim rings, no mute on the EA-260 (and a very plain trapeze tailpiece), they're the same bass. That one's just older, and looks nicer - and more like the Riviera, which it was intended to replace. Anyway...
Yes, you can fish things in and out a pickup hole, or an F hole - whichever you prefer. For the jack, I think the F hole might work a little better for you. But, for goodness sake, tie, glue, or otherwise fasten a string or something to it
before you pull it out. You'll die of old age before you get it back in place, otherwise. I've seen people use an old jack with a string attached, too; that seems to work very well. The same goes for anything else you decide to pull out of that bass. Make sure you have some way to pull it back to it's hole first. And yes, it's a pain in the ass; which is why most techs cringe when you show up with a hollowbody anything. As has been suggested, try a couple good squirts of DeOxit, or a good electrical contact cleaner; followed by lots of knob turning/switch flipping,
first, before you start trying to fish things out..