The other guess (or maybe another way of describing the same part) is that there is a ratchet-type latch that--unless worn or broken--isn't moving freely. It should click into place whenever winding of the spring is stopped. The spring is wound by rotation of the spool when line is stripped, or manually by grasping the cover as if taking the lid off a jar. There is a release mechanism as well that could be stuck, or damaged/worn.
Nice reel. I forget if H-I automatics were contract made for them by Martin, also of Utica.
Nice pics on the site but very poor description reflecting ignorance, disdain or both for fly fishing as it developed in the U.S. Actually, what "doesn't work very well" is a large arbor reel and superduper graphite fly rod for catching 5" trout, sunfish, bass and so on. Or, really, any fish that has no chance of running more than three feet because of its size or the size of the water it is caught in.
Autos suit and "balance" the heavier bamboo and then fiberglass rods of the time. They were popular and used for multiple duty in boats, ponds, and brooks when a reel was mostly a line storage device and fish were played with the line hand and intermittent winding (automatic or manual) to recover line. A drag wasn't needed, and even if somebody thought it was or made good pictures and advertising copy, it still wasn't needed. Neither was a lot of other technobabble high priced equipment, which still isn't in many of the situations where it is used.
Auto reels were inexpensive. As a practical matter, they would probably receive little care and attention, the annual cleaning amounting to a good soak in the bilge water of a boat and a swipe through the pond. The worked until they broke, and then you got another one. Or they worked until they needed a little fixing like adjusting the line trigger, and then they kept working.
All of mine still do and I bet you'll get yours going.
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