Everybody makes his own experience, I'm overall successful with the pull/push method, and not very much with any more aggressive solvents beyond a rinse solution - nozzle rocket whatever
Both techniques as described above can work. In the days before the R260 and R2880 era, Epson printheads were more durable/tougher and could take the push pull techniques and survive hard pulls and pushes. The newer printheads however are more fragile and the ensuing risk greater. So keep in mind that the generation of the printer is going to warrant what is tried with the attendant risk level.
The 1400 belongs to the era of a more fragile printhead. In fact, cracking or delamination between the black and yellow adjacent channels is a known common failure mode of this generation....just a design weakness carried over to today in the Artisan 1430.
Clogs can occur at the surface and also internally. On the surface it can be due to thickened ink and a normal clean and wipe will fix it. If it is dry, the rehydration technique will fix it especially with liquids that can creep well. However, if the clog is due to ink drying deep inside the printhead, clearing it can be difficult.
Here's why.
Imagine a very skinny long tube. Now imagine ink that has dried up in the middle of it and has form a blockage. There is some air to both sides of the dried up clog. Now because the tube is skinny, any liquid that is introduced to the tube, due to surface tension is going to form a complete column. When you try and force liquid in, the air in front of the incoming liquid is going to get trapped. So the air keeps the liquid from reaching the blockage. How to fix this? Forcibly by high pressure? Not a good thing.
So what is this pull and push technique talking about, is it the pressure that is working........Not really. By pulling first, you generate a vacuum and when this vacuum is released, and liquid enters, it has less trapped air thus getting deeper along the tube. Doing this multiple times might allow the liquid to "creep" deeper inside...or get moved inside. You need to understand what a vacuum really does. The aspect that the tube and syringe is directly above the head allows this technique to work. Keep the attaching tube as short as possible to the point that there is minimal volume and be somewhat gentle intially. You may need to try multiple times.
Some deep thought might allow you to figure out how this could be more effective than just pushing. But the principles are laid there on the table.....this is no BS. It is based on fundamental physics.
In any case, I have laid out the scientific principles from which you can develop ideas about how this technique can help.