The circuit, once you know how binary data is sent to the N64 video output chip, is pretty straightforward:
The video chip has a 7 bit wide data bus, a clock line, and a sync line; data is valid on the falling edge of the clock, data is 4 words wide, and the sync line is low on the first word, high on the others.
The first word contains 4 control lines for the video output, the three other words are the R, G and B values.
A shift register takes the inverse of the sync line as its input and it is clocked with the video chip clock; the output of the first 4 bits of the shift register is connected as a clock source for the 4 registers. In this way the 4 registers are clocked one after another, thus clocking in their data in the proper order.
The output of the three color registers is converted using a simple R2R DAC ladder.
You finally connect these control lines and analog color outputs to the N64 video connector, plug an RGB compatible SCART cable (a GCN one should do it) and voilà! RGB output is done.