Just some tips for TS. I've did this on a friend's car before on his 6 pot...large surface you can use wire brush or dremel those smaller area where the DREMEL can reach you can use the fine tip.
Before you do all the above, try using a degreaser to clean the caliper thoroughly 1st. Wear a glove and sock it in with an old tooth brush brush all those dirt and grease out. Then when you grind the caliper half way need to clean it then grind again, clean it then grind again.
For those really really hard to reach one I use sand paper. It was very hard to remove 100% of the old paint from the caliper. The maximum I will say around 85% ~ 90% can remove then I just paint the whole caliper in chrome silver. then clear coat it.
I suggest you don't leave the bare surface of the caliper out without a paint as there's no protection on the sruface after prolong heating, water contact and brake dust the surface will lost it's shine very fast and corrosion will happen also.
Those shinning caliper you see they are mostly painted with good quality chrome silver paint at paint shop. If you use can spray you need to polish the paint so that it's very smooth and have good reflection.
Good info, Tks for sharing!