mouse cursor moves by itself on Toshiba Portege Z30-A-19L

[valhalla_dweller]

I've been working around this problem for a while now, like six months but am getting a bit sick of it. It's intermittent too. Have tried the advice here which is a similar model of computer and similar problem but has not worked.

So as I said, it's intermittent. Was on a train trip last week and it behaved itself for hours at a time. Sometimes it moves slowly down to the bottom left and I can fight it enough to click on things. Today it is moving aggressively to the top right. When it moves quickly rather than slowly I can't do much with the PC and have to basically disable things and plug in an external mouse. I love Linux Mint, no problems on my desktop, would like this problem on the notebook to go away. (Got the fingerprint reader to work here btw)

When I type in:

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xinput list

The output is:

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⎡ Virtual core pointer                    	id=2	[master pointer  (3)]
⎜   ↳ Virtual core XTEST pointer              	id=4	[slave  pointer  (2)]
⎜   ↳ AlpsPS/2 ALPS DualPoint TouchPad        	id=11	[slave  pointer  (2)]
⎜   ↳ USB Optical Mouse                       	id=14	[slave  pointer  (2)]
⎜   ↳ AlpsPS/2 ALPS DualPoint Stick           	id=12	[slave  pointer  (2)]
⎣ Virtual core keyboard                   	id=3	[master keyboard (2)]
    ↳ Virtual core XTEST keyboard             	id=5	[slave  keyboard (3)]
    ↳ Power Button                            	id=6	[slave  keyboard (3)]
    ↳ Video Bus                               	id=7	[slave  keyboard (3)]
    ↳ Power Button                            	id=8	[slave  keyboard (3)]
    ↳ TOSHIBA Web Camera - FHD                	id=9	[slave  keyboard (3)]
    ↳ AT Translated Set 2 keyboard            	id=10	[slave  keyboard (3)]
    ↳ Toshiba input device                    	id=13	[slave  keyboard (3)]

I hate that silly "stick" in the centre of the keyboard and never want to use it, I think it is the source of this evil problem.
If I type in

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xinput disable 12

the crazy mouse behaviour goes away, touching that blue "stick" in the middle of the keyboard no longer does anything. The touchpad moves the mouse-cursor calmly and serenely around the screen without any satanic influence. BUT with the disabling of the "stick" the two clicking buttons above the touchpad are also disabled, so I can move the pointer calmly around but not click anything, so have to the plug in an external mouse.

It seems that the "stick" strangely is on the same circuit as the two click-buttons but the touchpad isn't. Any ideas how to fix this once and for all?