Straight to it:

My goal is to open the map as soon as a finger touches the right trackpad, and for the cursor to show up. Movement on the trackpad should drag the cursor around, and clicking the trackpad should place a marker.

In game I have

• "Left Click" -> place a marker.
  
• "=" -> Aim (this creates the cursor on the map and allows it to be moved with mouse movements
  
• "Tab" (hold) -> open the map, so that it's only open when Tab is being held down.

In Steam Input, I have

• R Trackpad Touch -> "Tab" Press
  
• R Trackpad Touch Extra command -> Delay 100ms, "=" Press
  
• R Trackpad Click -> "Left Click"
  
• R Trackpad -> "Mouse" (misc settings not related)

After a lot of fiddling, this seems to work consistently. The delay is critical to its success based on my experiments. If I touch the trackpad, the map opens, then a moment later the cursor shows up and I can move it around on the trackpad.

However, this fails to work if I'm also moving the left joystick. Instead, the map fails to come up, but the character continues to aim. It's as though the "Tab" input gets converted into a momentary input.