Here's your fix!!
I've had this issue for a while. I even had a jumper wire I made for the starter solenoid, when it would happen.
In this picture I found on the interweb, these are the wires that go to the starter relay. In Toyota's infinite wisdom, they put a relay to help alleviate the load put on the ignition switch. BUT, both power leads comes from the ignition switch.
So, if you take the thicker wire that is diagonal from the smaller black wire with red stripe. And cut it. Splice in a power lead from the battery with a 30 amp fuse to the end going to the plug. And just tape off the other end of the cut wire, since you won't need that. See in the picture.
I am linking the original post so you can read about it. Since I can't take all the credit. http://www.yotatech.com/f199/terrys87-86-4runner-2nd-chance-247386/index100.html#post52194586
What is funny, I was looking up something completely not related to "Toyota" or "Starter Issues" under Google Images, when I ran across this picture. So, I had to follow it up, and low and behold, it was the solution to an issue I had!! But, I didn't cut the wire, YET! I made jumper wires that would go from one terminal to the other corresponding terminal, except for the power wire. I didn't want to start hacking wires, if it wasn't the fix. If I don't have any issues, for some time, I will make it look better later on.