The objectives were curiosity (understanding how it works) and finding the missing pin so we can power up the module. The reverse-engineering isn't good enough to build a new one, e.g. I didn't figure out the capacitor values.
I don't think the silicone had any other purpose than keeping the components in place.
They did. Just not in aerospace until the mid 1960s when decent quality fibreglass (FR4) boards were available. The previous SRBP and Bakelite boards were fragile and/or hygroscopic.
PCBs during this time period were very brittle and fragile. The board itself was prone to cracking under high heat and the traces could easily lift off the board. Not a good fit for the hot vacuum tube circuits of the era. Zenith and other manufacturers often advertised point-to-point wiring as a feature for reliability
Seconded. I've worked with PCBs of that vintage quite a bit- both recently and closer to their era. They are absurdly heavy and fragile by modern standards, and were very prone to having the traces lift off the boards, to the point of being notorious for sudden electrical shorts. If memory serves, that problem persisted at least through the 1980s. I'm sure there was a technological development of PCBs that eased the issue; somebody who knows more on that subject may be able to clarify.
The Apollo hardware is a mixture of various technologies. Some pieces (like the Apollo Guidance Computer and the LVDC) used printed circuit boards. But point-to-point wiring was also very common. So PCBs existed but weren't dominant.
I was also very puzzled by this, I've seen pin mounting before in very old equipment but as you say PCBs were in widespread use by the Apollo mission. Perhaps a conservative approach to technology, or did it have a cost/reliability implication?
No, they weren't quite an established technology by 1960. Also multi-layer PCBs weren't a thing, and two layers do not allow routing for the component density.
The Apollo Guidance Computer and the LVDC used multi-layer printed circuit boards for the Apollo missions. I think the AGC was 7 layers and the LVDC 12.
IBM used multi-layer PCBs for the IBM System/360 (1964) so they were in use for some applications. But most electronics seemed to stick with two layers at most for a long time.
[1] https://ajhsynth.com/Lunar.html