It's great that you have this sorted out. As you've found, 'aftertouch' usually implies channel aftertouch. Polyphonic / key aftertouch is very powerful, but rarely implemented. You'll find it on high-end classic hardware synths, and some of the newer pad triggers or KMI MIDI controllers.
The left one has its red light on all the time. Shouldn't it just blink while the midi-in signal is there?
Yes. It's MIDI Input (left) and Output (right) activity. You could have a MIDI feedback loop (output somehow looping back to input). Or it could be as simple as a fast MIDI clock input, or an 'active sensing' message.
Some hardware keyboards (like Rolands) send a data byte every 300 milliseconds. It's supposed to prevent stuck notes if a MIDI cable gets disconnected. It's rarely used, adds some unnecessary overhead, and usually can't be defeated at the keyboard. There are ways to filter it out, but most people just ignore it.
The only problem that I've ever had with active sensing is that it freaks out my FCB-1010 pedalboard. The fix is to power-on the pedalboard with the MIDI In cable disconnected, then plug the cable back in.