I too use Mercury Quicksilver.. very much like brake cleaner. Both do the same, but I find Mercury Q to be a little better...
What I do is run a couple wet Quicksilver patches through, then dry patch, then one or two more (usually clean by three) THEN will put a brake cleaner patch thru to get rid of the Quicksilver that might be left as a film it's a little more of a degreaser/lubricator than brake-clean is Brake Cleaner is simply just a degreaser that dries clean & fast (best thing about it*) So yah, after that patch of brake-clean, dry patch right behind-- then one patch with a few dabs of oil, DONE.
It works very good for me, I've tried everything. Hoppes, bore-scrubber, all the rest just sits on the shelf since I switched. And one-can of Brake Clean/Mercury Quicksilver goes a longgg ways.. plus is in spray cans* Easier to use than a lousey open-top Hoppes (for example)
Try the stuff, you'll be impressed