Try hooking up a TSOP infrared receiver to the MCU

[probonopd]

https://gist.github.com/probonopd/c114ea42ea6fef5b6b6b6118ae49ebf8#gistcomment-2397945 suggests that the main MCU may be a Motorola/Freescale (now NXP) M68HC05 (HC05C12)

pin #37 (named TCAP), the MCU, underneath the VFD

Can we trace that pin to the J400/Q400 connector (measure continuity)? And can we connect an infrared receiver like the TSOP18238 there?

TCAP
This pin controls the input capture feature for the on-chip programmable timer. The
TCAP pin contains an internal Schmitt trigger as part of its input to improve noise
immunity

[probonopd]

We should probe J400 and Q400 (unfortunately undocumented even in the service manual) with an oscilloscope/logic analyzer while pressing keys on the Bose RC remote control. If the hypothesis is correct, then the "infrared" signals should appear there... indicating that we might be able to attach a TSOP there indeed.

(In other Motorola literature, it is confirmed that the TCAP pin can indeed be used for infrared remote control.)