The official ETA take on this is that you do not clean or lubricate the reverser wheels, but replace them.
The reason for this is that when they are new they have a factory applied lubricant which keeps thing moving nicely without gumming up.
The problem with cleaning them is that they then need re-lubricating, and the issue there is that if the wrong oil is used, or it gets into the wrong places, the pawls stick.
However, if my budget doesn't allow for replacement then I am quite happy to put them through the cleaning machine and then very carefully lubricate just the pawls with the smallest amount of 9010 that I can apply, and this works for me.
There is a special lubricant that you can use called Lubeta V105. This is a waxy lubricant dissolved in a highly volatile carrier. You simply drop the wheels in and then take them out again. The carrier solvent evaporates and leaves behind a very film of the wax.
The DIY version of this is to mix 9010 1:10 with naphtha.
I haven't tried either of these techniques but those who have reported their efforts on the inter-web report favourably.