E7440 mid-button above touchpad not working with Dell Driver

New E7440, arrived preinstalled with Windows 10 Pro including Dell Touchpad driver 10.2207.101.120. Touchpad two-finger scroll was not working but middle button from the 3-button row above the touchpad was working (I could open new browser tabs with it), so I opened Control Panel - Mouse and clicked on Touchpad Properties there. That immediately prompted me to restart windows so configuration changes (I didn't change anything) could take effect. After the restart, two-finger scrolling works but middle-button doesn't (no opening of browser tabs, and I also checked with a tool called KeyboardStateView that there is no key event generated when I press the button). Things I tried:

- changing things in Control Panel -> Dell Touchpad

- updating Dell Touchpad to 10.2207.101.121,A05 (latest version as of 14 Jan 2019)

- updating Dell Touchpad to 10.1207.101.113,A06 (old version from 2016)

- reinstalling Windows 10 from installation ISO

... and nothing changes. With Dell Touchpad installed I get two-finger scroll but no middle click, and without Dell Touchpad I get middle clicks but not scrolling. Is there a way to have both ? Maybe two-finger scrolling can be enabled without installing Dell Touchpad ?