Cool boomer. I always loved those tv boxes. Good luck on the repairs!
The volume difference in the tape deck does not sound like an azimuth problem to me. Could be, but I would rather expect lack of highs or lows on both tracks rather than a difference in volume. With a box of this age, especially when it's been sitting around doing nothing for many years, it's more likely that it's a (partly dried) electrolytic capacitor somewhere in the audio path from the tape to the pre-amp. Could also be a mechanical switch. I recommend cleaning all of those with deoxit, as well as the internal record bar, which is also a mechanical switch activated by the record button on your tape deck.
And while you're in there, also replace the rubber drive belts at the very least. They couldn't possibly be in a good state still unless they have been replaced fairly recently. Other rubber parts may also want some love like the pinch roller or idler wheel tires if your deck has those.