The simple answer is that baby oil doesn't not work as a booster.
I'm not a chemist but I can lookup and read some patents.
Baby oil (the real thing) = mineral oil/paraffinum liquidum/white oil (not precise but im still not a chemist
https://en.wikipedia.org/wiki/Mineral_oil)
1. Yasaka "Swelling agent of rubber for table tennis"
https://patents.google.com/patent/JP2008049094A/en They found that dibutyl sebacate
https://en.wikipedia.org/wiki/Dibutyl_sebacate (sometimes used in ice creams as a flavoring additive) is a good booster but also quote a patent application "As such an adhesion method, for example, Japanese Patent Application Laid-Open No. 2006-51328 discloses a method using an adhesion aid mainly composed of vegetable oil or mineral oil. According to this adhesion aid, the permeated rubber can be swollen and softened."
2. 2006-51328 is this one from Juic (they still make table tennis equipment)
https://www.j-platpat.inpit.go.jp/c...75544C842D349B05894E15CBD32CB0AA06BC8EE/11/en
"[0019]
In view of safety, swelling power and softening effect, the present invention has found that a material suitable for an adhesive auxiliary agent has a sufficient swelling and softening effect even in vegetable oils such as olive oil.
Examples of vegetable oils include soybean oil, rapeseed oil, sesame oil, camellia oil, sunflower oil, and the like. These vegetable oils are edible. Therefore, there is no fear that the table tennis player will be harmful to health even if it is usual.
[0020]
Also, it has been found that, from the viewpoint of safety, swelling power and softening effect, a sufficient swelling and softening effect can be obtained even in mineral oils such as white oil. As the mineral oil, paraffin, naphthenic, aromatic, Liquid Paraffin, white oil, petrolatum, petroleum sulfonate, or the like is used...
[0031]
[Example 2]
In this example, as in Example 1, an adhesive auxiliary agent was constituted only by white oil. First, to see the degree of swelling, a sponge having a thickness of 2.2, a hardness of 35 degrees, and an aspect ratio of 190 was prepared, and the adhesive auxiliary agent was applied to this sponge. After 6 hours, the dimension was measured, and the dimension was 214 in length and width...
From the test results shown in Table 3, it was found that, in the method using a vegetable oil and a mineral oil as an adhesive auxiliary agent, since the volatility is very low, a substantially constant hardness persisted for 24 hours. Also, this effect lasts for at least 1 weeks, and an almost constant state lasts from 1 months to 2 months. Therefore, it can be used even if it cannot be replaced for a long time...
The adhesion aid may be not 100% of vegetable oil such as olive oil. To the extent that the swelling effect is not impaired, stabilizers, fragrances, and the like may be added. A plurality of vegetable oils may be mixed."