The Vivitar won't sync with the 707 cos Sony uses a proprietary flash trigger (the hotshoe is a dummy). You either have to get a flash trigger (that ignores preflash), a slave flash (that ignores pre=flash) or the Sony's proprietary flash.
Umm...sorry, but when it comes to external flashes I'm a complete newbie. What do you mean by get a flash trigger (that ignores preflash) and what's a slave flash (that ignores pre-flash)? I'm guessing when you say the hotshoe is a dummy, you mean that it's just a place to mount the external flash and that it right? There's no way to send a signal to the flash to tell it when to fire and stuff like that, but if that's the case how does the flash know when to fire? Or do you have to somehow do it manually? And how does the Sony flash work? Is it expensive? Knowing Sony products, it probably is.