you want the inverter POWERED while the engine cranks? I'll assume you meant the opposite but first address having it powered while 'accessory' is on.How can I setup a relay to switch the power to my inverter when the ignition is switched to accessory, and keep power on for 5-10 seconds while engine cranks
If you remove the panel above where your legs are when you sit on the driver's side, there should be a 6 pin connector going into the key rig. there is a wire which, when the key is switched to accessory, pushes +12vDC. you can test this with a multimeter or you can track down a wiring diagram used for security systems. you can wire this either as your source of power for the computer, or as what switches the position of the relay to on.
as far as switching/ keeping the power off while the engine cranks, you can find in that same harness the "starter" wire. Relays can both be set up to be on unless powered, or off unless powered. If your relay is wired to be on unless powered, you can shut the power off while the engine cranks with this connection.
Sorry if i didn't even answer your question. give me more details if i misunderstood, and i'll see if i can help ya out.