Rodney, if it's short shank, it may not use that gear. however since the other style runs off the needlebar, if they fit, they should work also.
For reference, I'm pretty sure the older Kenmores that were top clamp were made by White. I know almost all the older Montgomery Wards machines were made by National under assorted badged names.
For the top clamp, a good clue is to see what the shirr plate and/or underbaider looks like (assuming it's original to the set) National and White feet may look almost identical (whites are 1/16" longer between the gap and needle hole) but the plates look quite different -
And for US made top clamp machines, figuring out what attachment fit goes a long way to figure out who made it.
Once they switched over to side clamp, that got uniform (they all match Singer) so it does not help, but makes getting attachments easy.
I was recently reading something about how Singer supplied the information for the Japanese sewing machine market, and that is why they all side clamp instead of top clamp machines. Have not verified that though, but it would make sense out of why Singer's method, which was different than all the rest, became the most common.