Cooling Fan Switch.
It should be the one you unplugged in order to install your jumper.
In my experience:
-These DO NOT respond well to seeing temperatures above operating temp. Furtherly, they seem to be more sensitive to overheating, the older the switch is.
Has your Y8 run hot and/or run low on coolant lately? Keep in mind, the stock gauge may not register a slightly higher operating temp.
-I have tried OE spec. replacement switch(s), and always have some issue with them (Shorter life, Fan ON or OFF at temperatures different than with an OEM part, or even zero Fan OFF function..).
That being said, I would buy a new one from Honda. It might cost a little more, but I'm here to tell you, it's worth it having to only replace it once.
Your 'wonky' heater output is strange, but could also point towards being low on coolant.
Keep an eye on your coolant reservoir, like daily (No joke). Determine if the car is using and/or leaking coolant. Next chance you get, do a Headgasket block test and see if the headgasket is compromised.
This all might seem like 'jumping the gun' towards a headgasket breech, but its worth investigating because if you catch the breech soon/early enough, it can save you time/money in the long run.