This is how it'll look like:

STEP 1 - CREATE TASK AND WIDGET

• Create a task called Toggle
• Add a Flash action with the text Toggling...
• Go back to your home screen and add a Tasker widget (not shortcut because that one's icon can't be changed)
• Select the Toggle task
• Give it a green arrow pointing right icon
• Accept
• Check how touching it will show the word "Toggling..."

STEP 2 - TOGGLE %ICON

• Go back to the task and add a Set Widget Icon variable
• Set Name to Toggle
• Set the icon to the left arrow pointing left icon
• Touch the little switch-arrows icon like in the video (you need to disable beginner mode in Tasker's settings for this to show up)
• Copy the icon's full path
• Go back to the task and add an AutoTools Text action
• Set the Text field to %Icon
• Set the Toggle field to android.resource://net.dinglisch.android.taskerm/drawable/cust_profile_exit_dark=:=
• Use the same process to get the green arrow icon's full path and append it to the Toggle field so that it's set to android.resource://net.dinglisch.android.taskerm/drawable/cust_profile_exit_dark=:=android.resource://net.dinglisch.android.taskerm/drawable/cust_profile_enter_light

%Icon is the variable we want to toggle. By setting the Toggle field to the value above we're saying that if %Icon is the red arrow (value on the left of =:=), it should be set to the green arrow (value on the right of =:=) and vice-versa. It doesn't have a value yet so it will first assume the value on the left of =:=.

• Add a Variable Set action where you set %Icon to the result of the toggle which is %attextresult(1)

STEP 3 - TEST

If you now go back to your home screen and tap the Toggle widget it should change its icon to a red arrow. If you tap it again it will turn green and so on.

In a real world situation the variable stored globally will more likely be a simple status, such as on|off or left|right etc instead of the icon path directly.
In that situation you can change the image accordingly, like this for example:

Code (Text):

A1. Flash: Toggling
A2. AutoTools Text:%Toggle   on=:=off
A3. Variable Set: %Toggle To: %attestresult(1)
A4. Set Widget Icon (right/green arrow pic) If [ %Toggle ~ on ]
A5. Set Widget Icon (left/red arrow pic) If [ %Toggle ~ off ]
 

This will make it easier for you to both select the appropriate image and also do other stuff in the task that depends on the %Toggle status.

Thanks for the tip Ratchet_Guy!