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0.12c would still be incredibly useful. Proxima Centauri in 35 years? Game changing.

for a travel time of 35 years, you'd not get very long at Proxima Centauri, because you'd still be doing 0.12c when you arrived

If you could keep an acceleration of 1g, it would take about 40 days to accelerate to 0.12c, and as much to decelerate.

The problem, of course, that with a Bussard ramjet, you won't be able to achieve nearly as much acceleration.

What would happen if you entered its orbit at that speed?

edit: according to https://rechneronline.de/g-acceleration/orbital-speed.php, if I got my numbers right (0.12 x solar mass star, .12c = 36000 km/s), the orbit radius would be 1230 km, so you'd be almost at the core of the star since its radius is ~ 100 000 km.

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