Bike pulses while applying the front brake. I'm unsure what the cause is Once per rotation of the front wheel, when braking, the bike pulses under me. The brakes are calliper rim brakes. 1. Swapping wheels out fixes the problem - so it is definitely wheel related 2. The wheel is true 3. I can't see or feel anything different on the brake track. 4. I have tried cleaning the brake track with degreaser and rubbing alcohol with no luck 5. I have also sanded the brake track to try to remove anything that could be on there. 6. I have measured the rim all the way round - exactly 19mm rim width the whole way around. 7. The pulsing does not occur when the brake goes over the rim joint. And it's still happening. Any suggestions?

Measure the rim in a more accurate way for starters. Even 0.1mm can cause a change in the braking power.
Also, with the bike resting on its handles and seat, flipped over, ask someone to lightly hold down the front brake while you slowly turn the wheel and figure out exactly where the trouble spot is and how big it is. If there is no visible difference, and you don't have the means to measure the rim more accurately, then it probably is the width of the rim being uneven. On the other hand if you find that it does not occur at the same spot every time, maybe the problem is elsewhere.
If you can, see if the width of the rim changes radially, fatter near the tire and thinner near the spokes. If the difference in this width isn't constant, it could be causing the problem