Paul, I've got a Synaptics PS/2 also, and am wondering whether you're looking in the right place for the Tapping function. For example, in your screenshot, it looks like your options TREE ISN'T OPENED, so you can't see all of your options. Why don't you try following my directions below to see if they will lead you to the control for Tapping. There are some other controls that will also help your mousepad's sensitivity issues. I'll highlight them for you:
Right click Desktop to open Personalize
Scroll down and select: MOUSE POINTERS; this opens the TOUCHPAD and MOUSE PROPERTIES page.
Select DEVICE SETTINGS:
Click the Settings bar:
Double-Click on Overview to open the tree and read the list of the multiple controls. (Double click on the + icon to open tree.)
TAPPING: Set to No.
SENSITIVITY: Double click on Sensitivity to open the tree and set the controls: (Double click on the + icon to open tree.)
PALM CHECK: (You can leave the Palm Check at the default spot, near center but a little toward Maximum. If mouse gets erratic, increase toward Maximum. If mouse is not responsive to certain clicks, decrease toward Minimum)
Light Touch (You can start with having it in the center, and adjust as needed.)
Click on Apply, and then OK.