I don't know if the grease manufacturer recommends it for the actual metal parts of the connectors, but it is certainly not good for that. The only place I would ever use it would be on modern weatherproof connectors that have rubber of plastic seals, like what you find on modern cars. Then I would only use a tiny bit on the plastic/rubber parts that seal on each other.
The Kz's came with connectors that were fully open to the elements. The grease isn't really going to keep out weather unless you use gobs of it. Then it gets everywhere. If it gets on the metal connectors, it may reduce the surface contact area. On a high-current connection, that will cause it to start heating up (since the current now has less metal to flow through), then that causes the grease to get liquefied and wick in further into the connection. After enough heat and enough grease gets in, the connector will need to be replaced. It's a headache I've been through several times on different cars and bikes. Usually it's the headlight connectors that take the worst hit, at least it's the most noticeable since the lights get very dim. If the connection doesn't use a lot of current, you might never notice a problem.
+1 on the Deoxit... which ever version dries clean, not the grease version. And watch out on plastic... maybe test on stuff you have in a junk pile first. It looks like it may harm ABS, but I don't know what Kawasaki used on switches.
If you are going to be doing a lot of harness work, I recommend the non-adhesive tape, like what the factory used, You can find it on ebay. Oddly, it costs more than the tape with adhesive.