Since this remote control unit (a UTB-YUB/GUB/TUB) doesn't have infrared, I couldn't just point an IR blaster at it. After some googling, I found a number of installation manuals and discovered the remote uses some sort of 1-wire (as in an actual single wire, not the protocol invented by Dallas Semiconductors) to do communication.
A few ebay searches later, and I found new remote control unit for $60 (from a supplier 20 km away), so I have a test unit that I can play with.
First step: Work out how this thing comminucates with the outside unit...
I've reverse engineered similar protocol for Fuji Electric AC Unit (RSGxxLUCA) using UTY-RNNXM wired controller, you can take a look at the source code at https://github.com/jaroslawprzybylowicz/fuji-iot and compare if goldens from the unit tests fit communication you captured.