Hello to you!
Gravol can indeed be used to calm dizziness and vertigo that occur in a context other than motion sickness
However, this mention on the packaging is used because these two symptoms can appear following a variety of causes (labyrinthitis, benign paroxysmal positional vertigo, viral infection, migraines, medication, surgery, etc.). It is then necessary to target the cause before treating "closed eyes". Once the cause has been identified, Gravol can be used, since it is one of the treatments available for the vast majority of dizziness and vertigo.
Your question about vomiting after taking it is very interesting! For a medication that is swallowed by mouth (tablet, capsule, etc.), the rule of thumb is that, normally, if an hour or two has passed since the medication was taken, it is considered to have been absorbed. However, this is an imprecise rule of thumb, since a variety of causes can vary the absorption of a drug. When in doubt, never double a dose and use suppositories!
For quick-dissolving medications, if swallowed, the same rule applies, but these medications are designed to be absorbed without going through digestion. In fact, if they are left long enough under the tongue, or between the gum and cheek, their absorption is almost instantaneous, once dissolved. Vomiting a few minutes later is unlikely to have any impact, since the medication "passes" through the gum to go directly into the bloodstream. It is therefore a good choice, like suppositories, for people who vomit frequently.
I hope that I have answered your questions,
Stéphane Villeneuve, pharmacist