Medicals probably start same time as security or a little before it. If your security is straightforward, it should be finalized quickly. I have visited about 25 countries, lived in another for a few years and also have military experience in my home country so it took about a month. Some people take days, some weeks.. others years. So, the only pattern would be the length of time to get an update after your medical would be an indication of how much security checks your file is going through. (My guess is anything more than a few months indicates it's in a more extensive review). When I did call to ask on my file, I was told the so called 'ghost update' was my agent switching my file's security step to passed.
Who knows though. This is all an opinion and guesswork. I've been wrong many times.. Some agents have told me one thing and others a completely different thing.