"but appears to say that 14 gauge wire will work with the 12 amp motor. "

The problem is not the motors draw when up to speed and running, it is the very large current surge required to start the motor.

Voltage drop under the starting surge will prolong start up time and lead to early motor failure.

Look for cord with a thermoset (rubber) jacket.
The first letters should be marked as type SJ, for Junior hard service.
SJ cords have a rubber jacket and rubber insulation.
They do not stiffen up in cool weather nearly as bad as the thermoplastic cordage.

Cords with thermoplastic jackets marked with starting letters SE & ST are not as good.

SJ cord will cost you more, but unless you cut it should last a very long time in household use.

I just gave up long ago and only use #10 cords with a rubber jacket in 50 foot sections.

Thanks, brickeyee.
Are two 50s a better choice than one 100 foot?

Maybe I will go up to 12 gauge, but I need to be able to fling the cord around while mowing.

Two shorter cord allow you to start using just one and then add the second as needed.

They are a little easier to handle and store (less size and weight each).
If you damage one beyond further use it is only half your total length also.

brickeyee offers some great advice. Personally, I would not go with anything less than 12ga for something drawing 12 amps.

OK, 12 gauge it is. Thanks for the advice.

I remember being frustrated at a job site once when two of my cords would not work and they only had about two years on them.

With folks on the clock I went and purchased the #10 cords.

I finally decided to just by #10 in 50 foot sections and as good as I could lay my hands on easily (usually junior hard use) without being really expensive.

Fifteen years later I still have the first cord, and while it has a few scrapes on the jacket it is doing fine.

I actually had some folks think they where water hoses once.