In this case, a complete rebuild of the calipers was not in order, as the bike has low miles and light use. With the calipers disassembled on the bench, an inspection of the brake pistons showed that they would clean up satisfactorily — no need to remove/replace the pistons. If the pistons had corroded to the point of pitting of the shiny surface, they (and their seals) would warrant replacement.
Below I'll reference a very thorough YouTube tutorial by Delboy's Garage on servicing a Nissin caliper, a Triumph in his case, but very similar to our VFR Nissin caliper. Del specifies some specific cleaners and lubes, but stresses that his choices are not magic potions, just use what we think is best. For example, he applied something called Red Rubber grease to the pistons after cleaning. I just apply some brake fluid on the pistons to help them slide back into their bores, just be sure to avoid getting any kind of lube in contact with the pads. He shows that this service can be performed on the bike, but I've removed the calipers as I'm also servicing the forks and upgrading the brake lines — and everything's easier on the bench, right? Many of Del's brake-related videos apply to our bikes, so consider them a good reference.
Here's our calipers assembled with EBC HH pads and ready for many more miles. TIP: Note the old brake line banjo bolt in place with a stack of washers — I do this to keep anything (dirt or liquids) out of the caliper bores during this service when the pistons will remain in their bores. If the pistons are removed for replacement, then this isn't necessary. The bolt will need to be loosened when pushing the pistons back into their bores! Then snug back up and leave in place till mounting the brake lines.