Edit 6/12- Added some info on Eddie's other basses and uploaded a new, bigger pic of the red Grabber. That stuff is toward the bottom of the article.Eddie's main live (and studio too, I'm assuming) basses are Gibson Grabbers. These basses were Gibson's answer to Fender and the import companies that ran the bass world in the early 70s. The series began in 1973 and was discontinued in 1982. These were Gibson's cheapest guitars at the time, and weren't made with the best materials. They were made to be assembled fast and cheap: There is only one pickup, a Fender-esque bridge dissimilar to a typical Gibson bass of the time, and the neck is a bolt-on and made of maple.
Still, there were some innovations with this bass. The big one is that the pickup is capable of being slid up or down to wherever the player wants it- allowing for bridge and neck-like tones (and whatever between) with just a single pickup and a "grab"... get it? The Grabbers were Gibson's first bolt-on neck bass, and the maple neck and Fender-like construction give the bass a tone that's closer to a Fender bass than a Gibson (possibly deliberately). Despite being cheap and built quickly, these basses became Gibson's best selling bass ever.
Eddie's main Grabber is one that he likely assembled himself. It's got a blonde body and a Grabber or G-3 (G-3s are the Grabber design in a 3 single coil pickup, no grabbing involved configuration) neck whose beginnings/model are unknown. He also has a wine red Grabber that's seen less action as of late. There's a pic below.
Eddie has actually been playing guitar on a couple songs on the 2007-08 tours: Open Water and The Earth Isn't Humming. There is little known about this guitar besides that it's an Epiphone something (looks like an ES-350?). It may have some Variax/similar modeling in it because it's tuned down quite low for the Earth Isn't Humming and sounds very full. This could also mean that it's got a baritone neck. Of course, maybe he just uses really, really big strings (he is a bassist, after all).
6/12 Edit: Eddie's got a few other basses, most notably two Fender Precision (P-Bass) basses. The first is an American P-Bass that he's had since the band's beginnings. He's also got another Precision bass: a 5 string American Deluxe. These basses went along for the last tour, apparently mainly as backups for the Grabbers. He's also got a G&L bass, apparently an L-2000. The L-2000s have a slightly Fender-ish construction, but use humbucking pickups.
There's more to come soon. We've tackled pedals and guitars now, and logically the amps are next. There are plenty of other things in store that I won't mention yet, too. I don't want to shoot everything off quickly and then run out of things to post! That shouldn't be a problem though. Thanks for reading, and as always, if you find something that's wrong or that I've left out please let me know!