I do NOT and will NOT recomend using locktite on the ejector rod. As for why, try re-assembling a cylinder that has had the ejector rod locktited. This is a very fine pitch thread and getting the thread started is purely a matter of "feel". Lose that "feel" due to the locktite residue and it's likely that you'll crossthread the joint, which means purchasing a new ejector rod and a new extractor star and then paying a gunsmith to fit and time it to your revolver.
A much simpler and safer option is to tighten it properly. Start by filling the cylinder with fired casings to protect the extractor star. Then fold a bit of old worn out leather belt over the knurling and grasp that with some slip joint household pliers. Note, I mean the common 2 postition pliers, not channel locks. Now wrap the fingers of your other hand around the cylinder and squeeze with the type of grip you would use for shaking hands with a Marine Line Officer. Basically, firm but not stupid firm, this isn't a handshake contest with an enlisted leatherneck. What you are going to do is use that hand holding the cylinder as a slip clutch, so let it slip once the ejector rod is tight. If you find it shoots loose again, squeeze a bit harder next time you tighten it up. Final note is to remember that for revolvers made after 1961 it's a Left Hand thread. One way to spot the left hand thread ejector rods is that all of them have a narrow groove just behind the knurling wide enough you can snag it with a fingernail.