I have a few suggestions:
A. Change your fluid to royal purple, run it once and see where the purple fluid is coming from. You will get two main benefits, 1. the best and most protective diff fluid and 2. it's color will give you the same benefits as the dye. I agree with everyone else in that running it up on a lift is very dangerous and not worth the risk.
B. You may be able to run your car on a dyno ($90-$100) and see where the
oil comes out from using mirrors. You can use a mirror with a handle, what many techs use when working on cars. This is similar to what dentists use, just a bit larger.
I hope this helps.
Jacob