FWIW, the viscosity of the dashpot oil, in effect controls the "accelerator pump" effect, ie how much richer the mixture goes when you first open the throttle.
I did some experiments with different viscosities many years ago on my TR3A with H6 carbs; and found that straight 20 weight oil worked the best for me. ATF, etc. were a bit too thin : the engine didn't stumble but did have a bit of a lean bog. And straight 40 weight was too thick for my taste : smal movements of the throttle would produce bursts of power that quickly faded.
At the time, straight 20 weight was easy to find, but it's a bit harder these days; so I just use 20W50 (same as the crankcase). It works fine too.
Haven't done a similar study with ZS carbs yet, but 20W50 seems to work fine in the Stag.
Two other comments that most of you know but maybe some don't :
1) The owner's manual for the TR3 tells you to fill the dashpots every 6000 miles. The level they give is high enough that the oil will leak down the piston and lubricate the outer sliding surface. But this area doesn't need a lot of oil, so if you notice the level is down just a few hundred miles later, there's no need to top it off. The oil cannot leak out below the level necessary for proper carb operation (on a SU carb).
2) However, the ZS carbs do have a seal that can allow the oil to leak out below the required level. It's a simple O-ring, but the books don't tell how to replace it. If your oil level goes down low enough that you cannot feel the resistance as you put the cap in place, then you need to replace that O-ring.