@jgeorge So cool!
https://www.reddit.com/r/whatisthisthing/comments/1e960ti/ibm_audible_random_timer_vintage_electronic/ has some good ideas.
Have you tried running it? The length of the random intervals might give you an idea of its intended use.
I love the way they put some perfboard into the PCB design and used it with the bodge wires! Maybe it's a prototype, if they were so confident they'd need to bodge it? :)
Anyway, such a neat find, and some very cool archaeology by you.