The burn-off circuit is a separate relay that the ECM commands on for a second or so when the ignition first turns on (or is it after a shutdown - I forget). In any event it's a relay you're after.
Take a close look at your connector pins on that MAF before you spend too much money on it. Make sure the pins and sockets fit tight with one other. Scuff up dull metal with a rolled up piece of sand paper. Urge the sockets closed with a pick probe. Dope the socket with dielectric grease. Hook it back up and give it a try.
I don't recall exactly where the MAF relays are unfortunately. Trace back from the MAF connector - they should be nearby.
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