I was fiddling with the pressure-sensitivity settings in System Settings / Hardware / Input Devices / Touchpad and quickly discovered that my older hardware, unsurprisingly, doesn't support this level of input detail. That's fine.

The issue is, having reset the sliders to 0, I wasn't re-granted tap-to-click functionality. Everything else works as it should, but single and double finger taps go unregistered.

I sniffed around touchpadrc hoping that I'd locate an =0 setting that I could nullify completely and restore whatever the default was, then I went off and tried a somewhat more intelligent mission to actually find out what the default configs look like, but I started to feel like I was just getting further and further from answering the question.

I'd be surprised if it mattered in terms of resolving my issue, but there might be a bug here that doesn't turn up on newer hardware so:
Gateway NV75S
Windows labels the touchpad ELANTech
Operating System: Parrot OS 4.11
KDE Plasma Version: 5.20.5
KDE Frameworks Version: 5.78.0
Qt Version: 5.15.2
Kernel Version: 5.10.0-6parrot1-amd64
OS Type: 64-bit
Processors: 4 × AMD A6-3420M APU with Radeon(tm) HD Graphics
Memory: 3.3 GiB of RAM
Graphics Processor: AMD SUMO