intermittent brake warning light coming on

you really don't need to disconnect the battery. unplug the switch/sensor form electrical, suck out most of fluid in master cylinder. on second pic there are two prongs you may have to take a long screwdriver to push the prong in to get the switch out. then remove it. install new one and refill reservoir. yes there will be some fluid drop out o fmaster so put a small pan there to catch it and don't get any fluid on paint it will eat it uup.

Can I just re-fill the reservoir with the fluid I take out (assuming I keep it pristine) when finished? Don't have to bleed the brake lines or anything?

don't be so cheap send the extra $5 for a quart of brake fluid to refill it. Fluid has to be changed every so often anyhow

You don’t need to even take the cap off the reservoir. Just pry the old switch out with a screwdriver. But the switch - look at it - and you see all you need to do is pull it out. Push the new one in and plug it in.