Would this Elgin have been considered as a pocket watch or wrist watch?

Wayne, this style was intended for dual use as a pendant or wristwatch. The Dubois/Depollier Watch Case Co. even had a patented case where the lower eyelet could fold into the case body when worn as a pendant. An example of the latter is at this LINK

i just presented my 16 year old niece with an illinois version of this style watch...

i have to get the numbers again to ID it.

I am looking for something to use for a bracelet for her watch so she can wear 'either-or'..

I bought her a chain so she can wear as a pendant...

Is it better to wear as a pendant with the attachment in the bow or on the other side??

Wear it on a chain hooked into the loop at 6, easier to tell the time that way, all the wearer needs to do is tilt the stem side up slightly and the dial is in full view.

I have seen women mostly wear them the other way, for dress. It's better to wear them as John mentioned, so it's easy to see when you tip it up. I think it's a statement thing.
Showing off the watch, and not much care about looking at the time. I have used them both ways myself.

Here is the watch...

and the movement

Back to my copy of the reproduction of the 1927 Sears catalog. Here's an illustration of a similar watch with an expansion band attached; this one has "12" at the usual place for modern wrist watches. The next page has an illustration for a ribbon band for the same watch.

Here's the ribbon band, now if you can find the fittings.....

Some of these "wristwatches" in the early days were made from small OF pocket watches. It's pretty obvious when you look at them to spot the ones that were..

If you'll go to the Very Tiny Walthams Wristwatch discussion you'll see pictures I posted which show a very early Waltham, a "real wristwach". You'll also note it's fitted with a silk band with matching 14K clasp. Very similar in style to some of those in the Sears catalog on this discussion.