I'm a fan of dark sky lighting whose primary rules are to illuminate only areas that need it and to only shine lights downward. I'd follow those rules and attach downward-facing lights to the beams or slats inside the pergola. You could use surface-mount, weatherproof electrical boxes (though there may be fixtures with integrated boxes - dunno) and hide any electrical conduit above the slats and beams.

While lighting the posts would provide no useful illumination, you could use surface-mounted boxes with holes cut just large enough for rear conduit, run the conduit up to the top of the pergola, and attach downward-facing sconces to the boxes.

-- amateur (obviously)

Ah thanks for the information on dark sky lighting, I am embarrassed to admit I wasn't aware before. It's unfortunate though as I do love the look of up/down lighting to highlight the beautiful redwood posts, but I would start looking for more options (downward facing). Hopefully something low voltage too but for some reason it's so difficult to find.

• Bronze 7" High Outdoor Dark Sky Tube Light
• Poseidon Bronze Tube Downlight 6" High Outdoor Sconce
• 12V LED Light Bulb 7W 630Lm AC/DC 12-24Volt Low Voltage E26 Base (2700K Warm White)40-60 Watt A19 Bulbs
• Low-Voltage 60-Watt Landscape Transformer

You could put the lights on the insides of the posts to illuminate the seating area.