Having posted earlier, I said I had this problem: On switching to or starting a new application the cursor becomes invisible. It can still be seen to operate in that things under the cursor, like the dock, will respond however the cursor itself is invisible until one of a number of gestures/key combinations are used like showing workspaces, then it becomes visible again for a while.
I
fixed my problem with an NVRAM reset as described here:
https://support.apple.com/en-ie/HT204063