What the thread establishes
The answer.
The thread confirms that fuki-urushi is a sound entry point because it teaches curing behaviour and basic handling before committing to coloured coats. For the Oryoki bowls, simple brushing of black and red urushi directly onto the wood is a legitimate and workable approach, though it will require test pieces to dial in brushing, curing, and sanding. On dilution, one commenter gives a concrete sequence: the first coat at a 50/50 mix of urushi to thinner, the second at 75/25, and all subsequent coats in straight raw lacquer. Another commenter frames the purpose of those early thinned coats as penetrating and sealing the wood and revealing the grain, and notes that a coloured urushi can be used in place of clear for those first coats to show the grain in the chosen hue. テルペン油 is confirmed as the Japanese word for turpentine, though at least one practitioner uses naphtha (white gas, camp fuel) or kerosene as the diluent instead.