I had a gas tank rust out under the straps on our 86 GN a while back. Came out to the garage one day, smelled gas, there it was dripping out. Had to replace it. Painting under the strap is a good idea. I use satin black on the areas under the car that were black and no gloss under the car or in the engine bay because a gloss finish hides things that are wet..ie oil, coolant, water, other things and you cannot see the source as easy.
What I find hardest about detailing under the car is finding the proper stopping point...ie do you paint all the areas that were one color with that color...or do you do them all the same, do you stick with a brush in hand that is 6" long or put a socket extension on it making it 26"....lol For a perfectiionist it's tough to quit until the entire thing is done.
One reward for the time and effort is when you do not have rust over many years of ownership if you did it right and then when you take your car to that occasional car show where they not only judge the exterior, but also inside the engine bay and under the car then you get the last laugh.