Yeah, you drive the TX side.
High-impedance mode is when an IO pin is not being actively driven high or low. Most commonly, this is when a pin is set as an input, or when a driver of some kind is switched off (e.g. when on a bus, idling; it needs to step back and do nothing so that other devices can communicate). It’s not uncommon to set an MCU’s outputs to high-impedance (=changing them to inputs) when idle, as this saves power compared to driving them to a high or low state.
As others have already alluded to, it also depends on what kind of bus it is. You can have buses with open-collector/open-drain outputs (bus is pulled high by default using pull-up resistors, and only driven low by the outputs), or push-pull outputs (inactive devices go high-impedance, and the active device actively drives the signal to high or low; a pull-up or pull-down resistor is optional, to give the bus a default state).
Your transmission line model is completely wrong. You show multiple capacitors in series, which is not correct. A transmission line has resistance and inductance in series, capacitance in parallel. And that’s just talking about the parasitics of the transmission line; any added capacitance to ground for filtering, series resistance, series inductance for filtering, or parallel resistance for termination, are in addition.*
It’s very unclear in your description what is doing what. Is the PCB circuit shown the transmitting or receiving MCU?
If I understand your original post, the second scope image is when you’re probing the same signals at the end of the ribbon cable, without the receiving MCU connected? Since you cropped the screenshots
, and didn’t otherwise provide the scope settings, we have no idea what time base you are using, and thus how fast this signal is. But bear in mind that standard 28AWG, 0.05” ribbon cable has around 48pF of capacitance per meter, between adjacent conductors (in the typical alternating gnd-signal-gnd configuration). The conductor itself has about 0.24 ohms/m resistance and about 0.5μH series inductance. This gives a characteristic impedance of around 100 ohms. This is fast enough for extremely fast signals, provided the termination is correct. I can’t imagine your boiler is producing a signal anywhere near fast enough to exceed the cable’s capabilities.
For push-pull: A 100 ohm series resistor on the transmit side matches the 100ish ohm characteristic impedance well. Then you terminate the receiving end with two 200 ohm resistors: one to +3.3V, one to ground.
See also
https://www.eevblog.com/forum/projects/how-many-mhz-can-a-1-27mm-ribbon-cable-handle/*Series capacitors in a signal line are used to block DC, creating AC coupling. That’s common in e.g. analog audio, but not sensible with standard digital logic, which is normally 0V as the lowest voltage, and positive 3.3 or 5V as the highest. AC coupling shifts the voltages so that it’s centered around 0V, with equal excursion to positive and negative voltages. For example, a 0V/5V signal becomes -2.5V/+2.5V.