I have to do a brake fluid flush soon on my car to keep things fresh. Here's what to do:
Buy this:
https://www.amazon.com/Mityvac-MVA6832-Clamp-On-Auto-Refill-Kit/dp/B000K1KPK4
This will keep all the fluid ready to flush without you having to keep an eye on the level. (I work by myself most of the time, so no one to help watch!). I havent tried mine yet on the ST, so you might have to get creative to prop it up in the remote fill reservoir.
Your current fluid should be slightly darker than the new, so you should be able to tell when new fluid comes through. You can let it gravity bleed. You can pressure bleed (hold pressure, have a friend open the bleeder to let the pedal pressure push the fluid out, close the bleeder when the pedal is at the floor, then repeat). You can vacuum bleed with a shop air actuated mightyvac or a hand pump, whichever you have.
No method is better than another, gravity is obviously the slowest. Do not just let it squirt out of the bleeder! its shaped like a pointed barb for a reason, to accept a clear hose to monitor the fluid flow! If you dont have anything, a local parts store should have something. If you dont have a local parts store, walmart should have fish tank hose... lets hope you dont have to go that route
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You can start at any wheel, but I would start at the furthest from the master cylinder [RIGHT REAR] in our case then alternate to the closest. Again, it really doesnt matter since its a "flush".
The other part of this equation is swapping the lines with the least amount of fluid loss. With stock rubber lines, you can use a fluid clamp or even vise grips to gently pinch off the line, then disconnect it from your caliper. Assemble the caliper side and get read to remove the clamped rubber line. Get some nitrile gloves on and remove the rubber line. Have a pan, baking sheet, whatever under your line and drop it when it comes loose. Wind the new line onto the cars hard line and tighten it down. Clean up any spilt fluid immediately with brake clean, alcohol, etc.
Let me know if you want to know anything else!