I guess I would not really matter Father Bill. If I were doing this I would insert the safety pins perpendicular to the length of the stabilizer.

Or in other words up and down relative to the kilt and following along the line of the pleats.

The idea is to catch the stabilizer. Then when you pull on the pleats you should see if the pins try to move indicating that the stabilizer is there and trying to take the stress. If the pins don't move or show signs of being stuck through something inside the kilt then it would be a good bet that your kilt does not have a stabilizer.