Okay so I know in some instances, people get shot here for asking what appear to be stupid questions. So if this comes across as stupid, please don't shoot...

But where does Sinestro's Wave 3 yellow lantern come from? I've looked high and low and I can't find it referenced in any comics.

Why did they give Anti-Monitor a cape? A looked over Crisis on Infinite Earths because I thought he did have one but alas he does not.

That was the look of Sinestro's lantern in the Sinestro Corps era.

I think it was a concept lantern that was never used.

Now that you mention that, I went to look for a comic picture where he actually has the lantern but I didn't find one. I think it's just an assumption that every lantern of every color has a lantern but unless you're Larfleeze or the Indigo tribe, you're not carrying it around all the time.

The BAF Anti-Monitor was based on his look in Brightest Day, which did include a cape.