I have had good results with a very light side damper oil which has resulted in better rear grip on a medium to good traction asphalt track here.

I was running thicker damper grease back in the day, like everyone else until one day my car was much better than it had been.
When I pulled my car off the track I found that the side damper had come loose on one end so I was running with no damper.

The car was great everywhere except in a switchback "kink" section where it was very uncontrollable. It would oversteer back and forth.

I put the damper back on and hated the way it handled, same as it had been before, loose out of turns and loose in the quick "kink" section but not oversteering back and forth, just looser in whichever direction I first turned it.

So I started playing with lighter and lighter damper oils until I found the best balance between oversteering back and forth (lube too light) and just loose in one direction (lube too heavy).
I now have a car that is very very good through the kink and excellent coming out of corners.

My TRF 102 has 3000wt gear diff lube in it right now.

That's my experience with side damper lubes.

The front of my car is stiff with black springs to kill steering also and needs to be turned with braking.
When it's right it's been very good like this.