You don't have to work in a major pharmaceutical company to gain experience working in pharmacovigilance. There are a number of pharmacovigilance service providers that will employ health care professionals who are looking for non-clinical jobs in the area of pharmacovigilance. Here's a list of some of those companies (many of these companies are also contract research organizations or CROs):
* 4G Pharmacovigilance LLP
* ii4sm International Institute for the Safety of Medicines
* Pharm-Olam International
* Synowledge LLC
* BioSoteria, Inc.
* BPI Service GmbH
This list can be found on Wikipedia here.