2003 highlander will not start and then after it sits for several hrs starts on 2003 Toyota Highlander

Mechanic has changed starter twice, battery, ignition and all wiring in the relay. Can't find anything else wrong.

Asked by for the 2003 Toyota Highlander
I might be mis-reading the question , but is it not CRANKING or cranking but NOT STARTING (running)? If it's not cranking , has the neutral safety switch been checked?
If you turn the key to start it does nothing. All the dashboard lights work there is definitely power coming from battery. The only noise you can hear with the hood up is some ticking coming from the fuse box. I am not 100% sure but I think I remember him saying something about the neutral safety switch. The problem is that it starts once it sits awhile so the mechanic is limited to what can be checked. Thanks for the suggestion, if you can think of anything else, please let me know.
If you've had someone turning the key while you're under the hood listening to the clicking noise make sure it's the fuse box as you think it is and go from there. You might be heading in the right direction. I've seen faulty connections in fuse boxes , where just pushing down on the cover puts enough pressure at the right spot and the symptom goes away (only while pushing...needless to say the fuse box itself was replaced in that case because the area of the fault was not servicable). In other cases it's been loose pin connections so those I or the tech that got the job originally would fix it [replace or repair terminal ends].Anyhow , just another idea, I hope you find the problem!
Thanks for the input. I hope the mechanic can find the problem too!