I believe the 84/85 had the electric pump, but Honda dropped it in the final 86 year. I've owned two 86's and I believe that you could eliminate the pump on the earlier models, but not absolutely sure. Certainly if you have a full tank of fuel, it should run, pump or not. Another easy-fix problem was the vacuum petcocks which would leak air and stop working.
But.... this bike could be a money pit and the VF500's are EXTREMELY hard bikes to work on with limited and/or expensive spares. The carbs are very finicky and very hard to work on - likewise the rear exhaust is a huge problem to get to. VF's also have the cam-oiling issues and the forked-rocker problem, although the 500 seems much less afflicted then the 700/750. Final thing is that the 84 500's were subject to a crankshaft recall - most were fixed by Honda early on, but you would need to confirm this.
Very neat bikes (probably the best-handling machine of this genre and still a wonderful handler today) and a great little jewel of an engine. But not a good candidate for the novice home mechanic looking for a fixxer-upper. This looks like a $300 bike to me that you take home, do a few things to see if you can get it running, but probably punt and part out on Ebay and make a few bucks. (I'd view the owner's claim that he paid $1K for a non-runner on Ebay skeptically - if he did, he's a fool. Maybe five years ago, I sold both mine in near mint condition for $1500 each and I don't think they've gone up in value very much.)
- Mark