First of all, I would take your cat to the vet to see if there is an obvious diagnosis. Take video of your cat during an episode, and show it to your vet also. It could be helpful for diagnosing your cat.
That said, if no other specific cause can be found, your cat could very likely have feline hyperesthesia. While severe cases could lead the cat to self-mutilation, that is not the case for the less severe or more average case. You may see frantic licking, scratching, or biting without actually being at the level of self harm. Or it could be as mild as getting suddenly twitchy, especially the skin on the lower back, and jumping up and running, just like you describe your cat doing.
As quoted from https://healthypets.mercola.com/sites/healthypets/archive/2018/03/25/feline-hyperesthesia.aspx
In kitties with hyperesthesia, the skin on the back ripples from the shoulders all the way to the tail, and sometimes up the tail to the tip. The movement is clearly visible in some cats, but more difficult to see in others.
What many pet parents notice instead is the kitty suddenly jumping and turning toward her tail as though something back there is bothering her. This can even happen during sleep. The cat might also try to lick or bite at the area. Kitties with hyperesthesia also have muscle spasms and twitches, and tail twitching.
And as regarding self-mutilation:
In severe cases of feline hyperesthesia, cats will self-mutilate by biting, licking, chewing and pulling out hair. These poor kitties suffer not only hair loss, but often severe skin lesions and secondary infections from trying to get relief from the uncomfortable sensations they experience.
Since if your cat does have hyperesthesia, it appears to be a mild or average case, I think it's more likely your vet will just tell you to try to prevent the cat from having episodes rather than resorting to drugs, although I should note that I am not a vet, so you should take their word above mine.
Hyperesthesia is made worse by stress, so minimizing stress will help. Episodes can also be triggered sometimes by touching the cat in certain areas, especially the lower back, so if you observe these episodes are happening after you touch some area of the cat, refrain from touching that area.