Ethyl Acetate: how to store
In laboratories, ethyl acetate is usually stored in special ventilated cupboards that are furthermore typically designed to withstand fire. This is because you will typically store not just one but many flammable solvents/reagents in that type of cupboard.

At home, you typically do not have that possibility. However, the basic advice remains the same: store in the original container (if possible) and in a well-ventilated area away from spark sources. The original bottle should, in theory, be airtight enough — remember that the ethyl acetate must have somehow found its way to you in that bottle without having lost too much content.

I would strongly advise against storing in a closed drawer. As you noticed, a few months were enough for enough solvent to evaporate but stay in the vicinity for you to smell it. The amount of solvent you lose per unit of time is typically very small and if it can diffuse away it does not do much harm. But the closed drawer prevented it from efficiently diffusing away and allowed it to concentrate.