Wow, I'm glad to see someone saved it, I had thought it wound up in the dumpster with the rest of the strong-arms at Nassau. Ask them to reach out to the LIRR, the signal guys may have had one stashed around still. The last ones on the property were probably the ones from the old B Tower machine that was used in the signal learning lab at Hillside. The main maintainer in charge of those machines was called the "valve and locking tech", and several of the ones I knew would try to salvage and store components from old model 14's etc. to barter for parts with other railroads. I remember one gent working with the guys who maintained the Cape Cod rail bridge tower or Amtrak's Livingston Ave Bridge in an effort to secure parts for their older interlocking machines. The ones working now may still keep in charge with the retirees who may know where, etc. to look. Also, try the group running the Norwalk switch tower, they may know of someone who could help.
Screw releases served a purpose of preventing an operator from changing a route established with a train "tapped on" until a set time had passed. This way the train could stop, or if it couldn't, it would block the operator from throwing a switch in the route. Therefore many had different times, so like in a big interlocking or a yard, the time could be small, but if it was a place like Nassau or Harold where the trains were going at MAS, a longer time. They were encased in a glass jar like container with a hole in the middle for the crank to activate the timer. (and each one had a locked chain to prevent access to the guts inside by anyone but the maintainer) If the timer was started, the signal would drop to stop, it would run (with a loud buzzing noise that would alert anyone nearby that someone was about to get into BIG trouble), and then after the time ran down, you could restore the signal to stop and then change the route. This was done after the operator had reached out to the engineer to take back the signal, or the operator would be in BIGGER trouble if he dropped it in their face. Also, if I was taking a track out of service, I could display a signal over a route into the out of service track, put the signal back into the notch to drop it, and then "can" it and run the screw release. Once having done that, it was virtually fool proof way of protecting that track, as even if the power went out, no air, etc., there was just no way you could get into that route. Some of the newer Model 14 machines had the screw release mechanism set within the "apron", Jay and Brook are two that come to mind that had that. Instead of the big glass screw releases, you would turn a dial set into the apron that would control a group of signals (or traffic, some had that ability also) and had lights on either side. Some signals would take 1 light (30-90 seconds) or others would take 2 lights (90 secs to 3 minutes). Usually the dwarves/low homes and pedestals were one, the PL's were two lights. Keep in mind if you ran the clock on a train that was already a few minutes off, then they were officially late, and someone would have to answer as to why.
The last model 14 with screw releases if I recall was Hall, which was 2010 or 2011, not including the B Tower machine in the signal lab. All signals today still have some form of this, but now you just select "cancel" in the menu, and then watch it flash red as it runs time. With the screw releases you could at least watch it wind down, now you sit and stare and hope that clock on the wall isn't slowing down like you think it is.