So, if you don't mind me asking, what methods of divination do you currently do? I've got cards, and I do look for signs, but I'm pretty ignorant when it comes to divination of other sorts...
Tarot, a self-designed quote deck, occasional other methods depending on the particular question.
Again, I'm not familiar with Drawing Down. I will have to do research... but is it anything like invoking a deity?
Yes and no - depends on what you mean by invoking. The way I use the term Drawing Down, it means the priestess or priest inviting the deity into their body, and to - some level - influence what's going on. (There can be different levels: everything from a voice in your ear with additional information to a much clearer overlay where the priest/ess's personality is very much in the back seat.)
It's not something to do lightly, without appropriate training, or without appropriate support (and especially aftercare if something goes oddly - things don't need to go badly to have a long-term impact that may not be what someone desired.) However, in the right circumstances, and with that appropriate support, it can be incredibly meaningful and informative in building a relationship with a particular deity. (Again, from either side of the equation: I've had amazing experiences being the priestess doing the Draw, but I've also had really amazing ones being in ritual where someone else did the Draw.)
In terms of getting to know a particular deity, it's usually something that's one of the last steps in building a strong relationship, partly because there are some very real potential risks. (I don't mean 'everything is doomed' but more like 'it's a bit like driving a strange car on unfamiliar roads in a drizzle'. Stuff might be just fine, and you'll get there safely, but there's also a lot of unpredictability in the equation, and what might happen is affected by that. You can do stuff to improve the good outcomes, but some of that is more work than others.)
The exercise I realise I didn't mention, but have gotten a lot out of, is one the group I trained with requires - each month, students are required to study a given deity (deities the group works with regularly, or who for various reasons come up in group interactions more regularly, mostly) and write up a short summary - major associations, summary of major myths, attributes, etc. But they're also required to do some sort of creative project associated with that deity. People have done everything from art to poetry to music to gardening to creating an oil blend to .. well, you get the idea. It's often that piece - when we get our head out of the way of the relationship a bit - that can be particularly powerful and effective.