I had to go with the cut wires and yeah its a pain...
you could find a 'hot' hook up the 2 wires from stereo (contant & key'd) then try hooking up the spreaker wires till you find the right ones (then put the key'd wire from contact to a fused power so that radio isnt always on)

OR
What I would do to make life easier...
if you still can...
Wire the factory plug back on....
find a 'Wiring Harness" to fit the Runner and wire it up to the radio - you should be able to find a wire diagram on JVC's website....

the harness's look like Harness Page

See if this pic works....

Not sure if the site I gave has the exact one for you, but you should be able to find one easy enough...

- - you wire the plug from the JVC (you can get these from JVC - labled) to the wires on the harness then plug it into the factory harness - EASY BREEZY..
Sure easier than trying to find the correct speaker wires (some vehicles have multiple wires - more that the 2 to one speaker) for fronts backs then sides then the 2 powers (1 is a remote) not to mention the dimmer wire as well....

Hope this helps and isnt too wordy.........

(edit) WOW didnt realize you cut the plug off AT the plug......