I don’t think you’ll need to solder onto the carriage.
If you diode-check continuity from the printhead pads to the ribbon cable, I would guess you will find that they are directly connected.
My guess, from looking at this printhead carriage, is that HP has moved all the shift-register logic I am attempting to decode for the HP60 series off of the printhead carrier and into the printhead itself.
What this should mean is that you should see a 1 (or a few) ‘always on’ 16v power signals to the printhead, and the rest should be 1.5v or 1.0v logic signals to the printhead shift registers.
That would explain the very low pin count on the printhead, and the simplicity of the carriage logic.