Question about SKS Racing Compressor E.V.A

My bike also has the "thick" valves. When I used the pump for the first time, I also had a lot of trouble putting the clutch on; it just didn't work.
After a moment's thought and a critical look at the coupling, I discovered that it is possible to turn the union nut. I unscrewed it first. A rubber is inserted underneath. Depending on how tight you tighten the nut, the rubber is squeezed together and the cross-section of the opening becomes smaller and smaller.
So far so good... So I relieved the nut until the coupling just fits onto the valve, making sure that the open lever is just in front of the check valve. There is a small pin in the centre of the coupling which pushes the non-return valve in a little when the lever is closed, making it easier for the air to enter the hose. The whole thing didn't work the first time, but in the meantime it works quite well.
Whether this is what the manufacturer intended ... hm... no idea; but it worked for me.

For car valves you need a hose with matching coupling, see accessories.