I'm in the need of some armour.

I think they start showing up once you complete the first quest, around the same time the desert storm security system gets activated.
As far as I've seen, the desert storm doesn't show up until you've actually spoken with BOS for the first time.

I can kill that theory right now. I have seen a patrol on my first playthrough before even finding the place and on my second I have only spoken to Veronica and haven't been inside yet. Though I haven't seen any yet.

This is certainly false, storm shows during night before you speak to anybody from BOS.

Patrols come out when the storm is going on at night. Im not sure if there is a specific time they patrol at night.