Here is generally how i would go about teaching a new TCP with the 6 point method.
Point 1 - Square up your tool to your reference point so that you are as square as possible to the world frame, or have a printed grid handy to align to. This point will be used to position the Cartesian space around the TCP itself.
Point 2 - Move directly along the first cardinal direction of the tool. For welding, we typically do X as along the path of a weld, and Y perpendicular to a weld, so that Z is distance from the surface. Once this point is set, your Cartesian space is fixed along that axis, but able to rotate around it.
Point 3 - This will be the last point to minimally define your TCP, and would be the last point with a three point method. This will fix the direction of the secondary cardinal direction and the rotation about the axis defined by points 1 and 2. The exact positioning of point 3 in the direction of the axis defined by points 1 and 2 is irrelevant and not used in calculation, but there is no value in needlessly deviating.
Point 4 - This should be the same as point 1, and i usually teach both at the same time.
Point 5 - Rotate the tool a significant amount (30-90 degrees) and then jog until your TCP is back at your reference position but the joint angles are all different. The larger the difference of the joint angles, the better the calculation will be.
Point 6 - Return to Point 1/4 and then rotate differently than you did for Point 5. The exact direction does not matter, just providing a larger spread of angles for the system to use to triangulate where your TCP is.
As an additional note, i would get a printed grid and tape it firmly to a metal table with no chance of moving, and station it where the robot can easily reach and articulate. Mark three points on the grid, at least 6 inches apart in the shape of an L to define points 1-4, with 1 and 4 at the apex, 2 directly forward, and 3 to the left (we do it to the right so that Z- is away from the part, but to the left will most resemble the world coordinates. The robot will always follow the right hand rule). Orient the robot so that the weld tip is straight up and down perpendicular to the grid, and positioned at the center point. Define Point 1 and Point 4. Jog away from the grid, then move to the second point (forward, away from you and the base of the robot) and bring the TCP back to the grid and perpendicular to the surface to define Point 2. Again, move away from the grid and move to Point 3. You should always move away before trying to move sideways when teaching weld TCP because bending the weld wire while teaching messes up your TCP. Once you have taught 1-4 and returned to Point 1/4, then do your rotations. I try to rotate away from me as far as i can for Point 5, and to the side as far as i can for Point 6. Both of these will touch the same grid point as 1/4, but not perpendicular to the surface.
Last note, there are three different 6 Point Methods available, X-Y, X-Z, and Y-Z. This specifies what axes of the Cartesian space you are defining with points 2 and 3.