If we prevent that cell from being born, we will have a functional oscillator.
The red cell was born because it had three neighbors in the previous generation, so if we get rid of one of those cells, it will not be born to due having only two neighbors, so our loaf parent will work.
We can’t get rid of either of the light green cells because they are part of the loaf predecessor, but getting rid of the yellow cell would fix the loaf predecessor.
The red cell was born because it had three neighbors in the previous generation, so if we get rid of one of those cells, it will not be born to due having only two neighbors, so our loaf parent will work.
We can’t get rid of either of the light green cells because they are part of the loaf predecessor, but getting rid of the yellow cell would fix the loaf predecessor. To do that, we need to look one generation earlier.
If we do nothing, the yellow cell will be born in the next generation because it has three neighbors, so we can prevent its birth by changing this. The row above the yellow cell is the best region to modify for this purpose because the it is the easiest to modify by something that would not have interacted with the block-and-almost-loaf predecessor previously, so we can add one or more cells there so that the yellow cell will not be born due to overpopulation. Adding a cell in either of the gray positions would cause the cell just to the left of the yellow cell to be born instead, which would also mess up the loaf predecessor, but adding a cell in the light green position would work perfectly fine. In order to do this, we need a sparker.
Because our reaction would yield a period-twelve oscillator if fixed, this sparker must have a period dividing twelve (either twelve or a proper factor). For this reason, certain sparkers, such as Kok's galaxy, would not work due to only providing the correct spark some of the times when it is needed.
And this is how I independently discovered baker's dozen. (The linked wiki page shows additional stabilizations.) There are other ways of finding oscillators, but some of them also involve sparkers. For example, David Raucci has made a script that searches for ways to spark common active regions that result in the active region being formed again, resulting in oscillators such as this period-eighteen lumps of muck hassler.
However, the original example of blocks and sparkers hassling a still-life is not as uncommon as one might guess. For example, consider this reaction from jslife/osc-supported/s0018.lif:
We want to find a way to hassle the beehive without infinitely many gliders. One option is to use a sparker whose spark can replace the block. In order to figure out which types of sparks work in replacing the grin/block. Testing different options yields some that work (on the top row) and some that don't (on the bottom row).
Comparing the two suggests that if we have a two-cell leading edge, we need both cells to survive to the next generation, and of the two cells diagonally above and to the right of that two-cell leading edge, exactly one should be alive in the next generation. (This isn't exactly correct, e.g., 2bo$2b2o$2bo$2o$2o works, but this type of exception is unlikely to occur from a sparker.) We need a sparker that delivers the correct type of spark at a period dividing eighteen, and the aforementioned sparker turns out to work. It fact, it works with two relative timings, both of which are shown below.
There are other ways to stabilize this. For example, instead of trying to replace the block, what if we try to find a way to reinforce the block to save it from being destroyed. This works in other contexts. For example, a glider hitting a block from as close to the block's line of diagonal symmetry as possible ordinarily destroys the block, but the block can be saved by an interaction where it would normally act as a catalyst.
Let's therefore confine our search to oscillators whose period divides eighteen. We also need a oscillators that perturb a block, so let's investigate the blonker, which has period six. There is indeed a way for the block to survive being sparked without any permanent damage.