integrated turn signals and brake lights

The tail light is a separate bulb or element on the same bulb.  A tail light is not quite as bright as your brake light lamp.  If your tail lights are on and you apply the brake, the brake light lamp is brighter so you can easily notice that the brakes have been applied.

If you are at a stop light at night with your left blinker on, the tail light will be on.  The right brake light will be on.  And the left brake light will be blinking.  But the tail light will remain on steady.  The blinker will be very noticeable, because that lamp is more intense than the tail light lamp.

If you are having trouble getting to a hot non-flashed wire at your blinker switch, there is another way to do it.  It will require an extra relay per side of the car, and the side marker will flash opposite of the actual blinker.  Just throwing that out there in case it is very hard to find the blinker wire before the flasher.  The other guy had easy access to his flasher assembly.

From what I have been reading, he has a separate tail/running light bulb/element.  He was wanting to integrate the blinkers with the brake light bulb/element.

Integrating a blinker into a tail/running light, will not be very effective when the brighter brake light element is burning.  You won't really be able to see the blinker unless you are looking for it.

The diagram above WILL work just fine for your side marker lights.  Where it says to brake light wire, it should read to side marker light wire.