The 2001 Toyota Tacoma that won't start every now an then had a new STARTER installed rather than fuel pump. I was wrong on that. Why would a new starter make it not start every now an then?

I would guess a loose or poor connection. Have you checked and cleaned all wire?

With Toyotas, it's best to only install a new OEM or Toyota rebuilt starter motor. The internal solenoid contacts on aftermarket starters are cheap and tend to pit easily. This affects the ability of the starter to get the amperage it needs to start.