Battery drain issue

Yes, BUT........be careful. It is easy to screw up an ammeter because they are a SERIES device, so do this FIRST

Disconnect the battery ground, and put a large lamp bulb in series, such as a backup lamp or stop/ turn filament lamp. If it glows fairly bright, I would NOT hook up the ammeter and use the lamp instead

Make CERTAIN your multimeter is set up for the MAXIMUM current (amperage) measuring scale. If you are in doubt, post a photo of the meter, or at least the brand/ model.

With the multimeter set for maximum current, usually 10 or 20A, replace your test bulb with the meter. BE CAREFUL not to short one of the leads to something else

If you don't get a usable reading, carefully set the meter to lower scales until you get a useable reading

Good point, but most ammeters have a series fuse built in, mine is 2 amp so it'll blow quickly.