Incidentally, the lady in the tax office also had no idea what those fields in the offline software were referring to when I showed her the screenshot in my above post:
It’s this kind of thing that makes me unsure of the correctness of info given by the tax office sometimes when it comes to less conventional situations like ours (despite them mostly being helpful and friendly).
I did try asking her about the thread topic (work done by Taiwan residents while physically outside Taiwan) while I was there. This was another question she wasn’t able to give a good answer to and the conversation devolved into some frustrating back-and-forth where we were both talking about different things, but the impression I got was that (i) it would be possible in principle to disregard income earned while physically outside Taiwan, but it would require additional evidence that the income was actually earned and/or paid while outside Taiwan (e.g., entry/exit records, documents from overseas tax authorities, possibly notarized stuff) and (ii) this would be easier in the 183–300 day range to meet the <300 days requirement mentioned above.
No definitive answer, though – we were both getting a bit irritated with the conversation at that point and it didn’t make enough difference to me to want to pursue it. (She was also looking at it from the perspective of someone with a full-time employer, and she didn’t seem to grasp how somebody might work remotely for, say, a couple of afternoons while on “vacation” or outside Taiwan for two months.)