Tracking down a short

FWIW, Yes you should use an ammeter since what you need to know is the current draw. If it hasn't been stated here already, connect it in series between battery negative post & the neg cable with meter off.

Touch the negative cable to the battery post & hold it there. Now turn ON the meter & set to the highest ampere scale (10a or 20a on some meters). After waiting with the neg cable still touching the battery post for 30 seconds to time out the electronic timers in the car, remove the battery cable away from the battery post with the meter connected in series & measure your amps. If its not enough to show on the meter repeat the procedure on the next lower scale. Note: You must keep the cable in contact with the battery & time out the electronics every time you remove & reconnect the meter or you risk blowing the internal fuse in the meter.
50-60 milliamps(ma) is considered acceptable for most commonly equipped computer controlled vehicles today. If it's higher remove fuses 1 at a time & observe your meter drop. If no change or minimal, reinstall the fuse & keep going until you find the 1 that gets it under spec. Then that's your problematic circuit. Now you are only 1/2 way home! You need to find everything that operates on that fused circuit & check those components, circuits & sub-circuits. And don't open the door with the meter connected or the dome light will make the fuse in the meter blow! You can turn off or disconnect the light 1st to be safe if you're sure that's not the draw.
PM me with an questions if you'd like.

These vehicles are notorious for bad body control modules causing problems. You would need one with the same part # & calibration to replace it & they aint cheap. I have also seen trouble in the wire harness under the hood that wraps over & around the transmission near the air box. But it could be anything.
I hope this helps.