I had the same issue, but not on my 4runner. It was on my CRX. Intermittent click no start, changed starter, relay, wires. A week would go by with out a problem then click no start for a few minutes, it was SO bad that I had a wire permanently attached to the starter solenoid, so I could touch the other end to the battery terminal and finally be able to start the car. Months later I solved the problem PERMANENTLY! I've had two other cars before where I was never able to solve the click no start syndrome before I eventually sold them. But I stumbled on the root issue of why OLD cars get the click no start issue, even with new wires and starters. I permanently solved this issue on my CRX (if the 4Runner get's it I'm sure it will fix it too)
My realization was that the ignition lock has the starter switch attached to it with little screws, and it's twisted into switching on and off by a metal flat tip (in most cases) coming from the ignition lock cylinder, and with no available adjustments. Well over time the holes where the little screws pass through the switch widen slightly, enough to where the twist action of the lock cylinder doesn't twist the ignition switch all the way to make good contact with the "start" pins.
What I did and has started my car every single time for the past year, is that I LOSSENED (with out taking them out, yet) the little screws that hold the switch to the back of the lock cylinder and manually twisted the switch against the direction of the turning key (it will only move a few millimeters at the most but that's all you need) , then tested that the car starter at once, it did. So I tightened one of the screws in place and took out the other one to apply thread locker to it then put it back in and did the same to the other. I put it all back together and it has worked for over a year now, starts every time.
I was at my wits end when I did this, it was SO annoying, that's why I wrote this long winded description, It might help some of you. If I find a 4runner at the junkyard I'll take the ignition switch apart and take pics to show in detail.