Instead of a button with two parts, with a dividing line and then a small dropdown arrow, make the entire button a forced dropdown. That is, remove the dividing line, making it just a single-part button, so that clicking anywhere on the button drops the menu down.
Reason: There's no escaping the fact that you have to specify a protocol, so it might as well be a larger click target than just the little arrow on the right. The functionality of the left part of the current button is already provided by having the user press Enter immediately after entering host details, at which point a Quick Connect panel appears to take care of the missing info.
Also, clicking a second time on the button should hide the dropdown menu, not make it reappear (like clicking the arrow currently does).