I received your PM, and did post a lengthy reply!
The short answer is: cast on 20 stitches, using the US11...and knit for a full 5". Then, measure the center 14 st. If they are less than 4" wide...the US11 is too small. (yes, cast on 20 st because knitting more stitches 'sets' your 'hand'...and more stitches may work best to get the BIG PICTURE)
And you must achieve 'gauge' on a st st swatch, not garter.
Also, this pattern has vertical design as well (in the bottom portion)...so row gauge is a factor. So, lay your ruler over top of your swatch, mark 4" in height...and count the number of rows within that 4" space. But, Row gauge is not a critical as stitch gauge.
Back to stitch (width) gauge:
If your 14st is measuring, let's say, 3.75"...that means that every 14 st you knit, you are losing 1/4" in width. This can severely impact the sizing. For example: if a sweater is 160 st around in total...and you are losing 1/4" for every 14 st...that garment will be about 3" too small around.
If you can't get gauge with the US10.5 or US11...then consider making the size up. For example: if the size SMALL with US10.5 needle is gonna be 3" too small around...knit the size MED! It will end up being a size SMALL with the US10.5.
I agree, the US13 would not work. Some yarns just don't like it when you use a bigger needle on them. Certain yarns just like certain sizes of needles best. Together they deliver a nicer appearance, a prettier stitch, not too holey, not too compact like a braided rug.