Yes, most likely it is a vacuum leak.

But, also check the throttle position sensor, the idle motor (both long shots)...

and actually the battery. Yes, sometimes certain cars can get a weird idle when the battery is about to go. I've had it happen to my car, and I've seen it happen to several others.

Yes, it CAN be the battery. Trust me on this.

As per your description of the problem...

"It does NOT do this! Instead, it bounces between 500 and 1,200... Coming close to STALLING..

HOWEVER.

When I come to a _complete_ stop, it idles perfectly"

That exact same thing happened to my saturn, to my mom's Lebaron convertable, my brother's olds, my dad's 626.... in all cases it was the battery.

"Tutto fa brodo."

Todd Scungio
98 RS
15.173 @ 90.70 MPH

And also a 2011 Ralliart