You'll need some of these. Brake fluid is toxic and corrosive. You won't feel any pain if you get it on your skin but it's not a good idea. I wear these all the time now when doing mechanical jobs - most car chemicals are officially "bad shit" especially used engine oil which is a definite carcinogen.

This job turned out to be really messy with fluid leaking out all over the tools so I was pleased to have a large supply of these gloves.