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Your best option is to fix the existing wiring. The pump should not be running when the engine is not running. It's a safety feature so that if you roll the truck or get into a crash, the pump will not pump fuel onto a hot engine and start a massive fire. The Toyota service manual has a full wiring diagram that will help you fix it.
Next to that, and this should be your last hope option, is to wire the pump into some wire (possibly using a relay) so that it only runs when the switch is on, along with an oil pressure switch, so that it will only run with the key on and the engine running. That is the only safe way to do it.
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