Do the easy thing and disconnect, inspect, clean and reconnect all connections involved first. Start with the battery box, assuming you haven't already touched that area. Most MVs are not "turn-key", they need refurbished nearly everywhere and periodic revisits. It's not Whether or not to clean and inspect all the bits and bobs, it's When to do it.
In the case of the starter I noticed when running my grounding harness that all the wires down there were 1) close to the exhaust along with making a few bends, and 2) dirty as all get out despite having washed my HMMWV more than once (at the Syria Car Wash, for those that know it). Experienced lots of cursing and spitting out crusty bits that fell on me while I worked, on that piece. Cleaning up the starter area connections and checking that the wires are protected and not chafed will give you piece of mind, even if they don't give you your solution.
Bulldogger