So I was demonstrating the Trekulator to someone and at first it wasn't working correctly. The unit would power up but the buttons were not working. After a couple of power cycles the keys started working again and the = sign would now play the sound (badly as before) but would update the display with the result of the last operation. Yay. Seems to be holding after multiple reboots so fingers crossed.

I had another quick look at the speaker. When I first opened up the Trekulator I noticed that there were two short wires soldered to the PCB that had obviously been cut, and I just assumed that they were for the speaker. To verify this I watched the Computer History Archives Project video again and captured the following two screen shots:

The one on the left is from the unit with the working speaker, and on the right from the one where the speaker had been removed.  Notice the blue and white wires in both images almost certainly verifying where the speaker was attached.  Unfortunately for me this is exactly where I attached my speaker so I now know that wiring is not the reason my unit does not emit the "calculating" tones correctly. This will require further investigation, but then again maybe it will "just start working" down the road. It could happed ;-)